Here are your parts
http://www.appliancepartspros.c...ch.aspx?model=FSE747GES1

I am doing some guessing here as I cannot find a wiring diagram for this unit.

[COLOR="Blue"]For instance, would it make sense to substitute a thermostat that opens at about 250 degrees? If this makes sense, can you recommend a particular temperature and part number?[/COLOR]
You could run into problems here as the heater may start being controlled by the high temperature thermostat. These thermostats are just safety devices and their contacts will not last very long if the are switched on/off often.

[COLOR="Blue"]Or does the dryer shut down and stay off if the high temperature thermostat opens?[/COLOR]
No it does self reset. Opens at 285 and re-closes at 245 (re the -40 spec)

[COLOR="Blue"]1. The exhaust vent does not appear to be blocked. [/COLOR]
You could try the following to eliminate the venting for sure.
Unplug the unit and disconnect it from the vent system.
Now try a run.
If it now dries OK odds are the vent system needs checking/cleaning.
Be sure to check that the louvers on the outside of the house open correctly.

If you do not want any lint in the house.
Take a pair of pantyhose.
Put one leg into the other and then attach this to the dryer's vent.
Leave enough room so the pantyhose can balloon out like a windsock.

Both the above will let you check the temperature and the air flow.

Note: The above is not recommended for gas dryers due to carbon monoxide concerns.

[COLOR="Blue"]2. The cycling thermostat [/COLOR]
This is a possibility.
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3. The heating coil isn't stuck on, since the fuse didn't blow with the fabric temperature dial set at "air fluff."[/COLOR]
Your conclusion may be wrong.
Many units remove power through a set of contacts is the timer when in air fluff so depending how/where the element grounded it may only get power in a heating mode. Without a diagram I am unable to confirm this.
I would check it with a meter though often you can see the grounding point.

Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 10 to 12 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run on high and the thermostats cannot regulate it so the thermal cut-off blows.

Just in case it is not a grounded element.
With all the below the high limit will also have to be replaced.
Check that the belt is OK.
Check the seals (drum etc) in the unit. The air is pulled over the heating coils, through the drum and pushed out the exhaust. So any large seal leak will pull in room air and the cycling thermostat on the blower will run the unit hot.
Check that the lint filter is not coated with fabric softener residue which greatly reduces air flow.
Check/clean your vent system.
Check/clean the blower wheel.

If all OK you may want to replace the cycling thermostat as it's contacts may not be opening (welded shut). This can be checked by heating up the face of the thermostat. It will not tell you where it actually opens but at least tells you thet it does open. I use my soldering gun but heating it on a stove top element will also work.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.
4. When you start always short the meter leads together. This will tell you that the meter is working and if there is any 0 offset.

There is a good STICKY at the start of this forum about it's use.

do you mean I should connect a new thermal fuse to see whether it will blow?
Yes. This just eliminates the vent sysytem as a possible cause.
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Or is there a way to try a run that doesn't risk wasting another thermal fuse? (For instance, shorting together the pair of wires that normally connect to the fuse so that the dryer can run temporarily without a fuse, and monitoring the temperature in that vicinity while the dryer is running to see if it stays below 220 degrees.)[/COLOR]
You could do this.
I do not recommend it because there are lots of folkes out there that will just keep running it with the fuse shorted. Then when their house burns down they complain.

[COLOR="Blue"]What do you suppose is the purpose of the wire that connects the high temperature safety thermostat to pin R of the timer? Will it pause the timer when the thermostat opens at 285 degrees, so that the dryer will automatically resume when the thermostat cools off to 245 degrees? The other version of this model dryer lacks that wire, so I'm unsure of its purpose.[/COLOR]
I do not have a wiring diagram and do not like guessing.
I do have other Frigidaire diagrams and they are sort of backwards to what you say. The timer advances when the hi-limit or operating thermostat open.
I will try to explain, please excuse me if I loose you. One side of the heater is connected to L2 (black) (lets say left side)the other side of the heater (right side) is connected to the thermostats and then to L1. It is also connected to the R you refer to. When thermostats are closed you have L2 and L1 (240 volts) across the heater and it heats up. When a thermostat opens L1 is disconnected (heater cannot heat up) so you only have L2 on the left side. This voltage feeds through the heater so you also see it on the right side. And this now goes to R which drives the timer motor through a resistor which drops the voltage down to 120 for the timer motor. The heater does not get hot because the current draw of the timer motor is very low.



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I can't check the louvers on the outside of the house, since this is a condo unit. The building has a system of fans that continually suck air through the vent in the wall behind the dryer. I can tell the fan is sucking air, because it will strongly hold a sheet of paper to the opening of the dryer's exhaust blower.[/COLOR]
Sounds OK but you are pushing air out so I cannot say if the venting is OK just because it has some vacuum.

[COLOR="Blue"]Is there a way to test for blockage in the exhaust from inside the dryer, without detaching the dryer from the wall vent?[/COLOR]
No.
It is a pain but may end up your last resort. The order I list things is arbitrary so if finding out if it is a vent problem may be the last thing you do as it is the biggest pain in the you know what.

[COLOR="Blue"]I'm not sure how to check the seals for air leaks.[/COLOR]
It is just visual. The drum is actually part of a vacuum as the blower suck air through it so if you has a large air leak the you would be sucking in room air and the thermostat would then keep your heater on.

Sounds to me that you are doing a very thorough job trying get to the bottom of this problem.

All of the below are just educated or perhaps not so educated guesses as your problem has me grasping for straws.
Note: that I am off to the cottage for a week so will not be available.
You may want to start another post with a link to this thread. If other regulars on this forum see that someone has been working on a problem they will not have the time to take a look at all the posts. So having a post without my name on it should get you some additional input.

[COLOR="Blue"]3. Replaced the cycling thermostat.[/COLOR]
Si we can assume that the cycling thermostat is OK.

[COLOR="Blue"]After doing all that, I tested the dryer Saturday morning (without a load of laundry).[/COLOR]
I agree with you that this also seems OK.
Just one question, was there any heat from the unit in Air Fluff?

[COLOR="Blue"]the dryer had been set only at "low" heat. The top of the dryer was uncomfortably hot all over, not just in the rear corner.[/COLOR]
This points to an air flow problem.

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Would the moisture of the afternoon load have made the difference between the morning tests that passed and the afternoon failure?[/COLOR]
Moisture will make a difference as to how often the heater is cycled as it takes more energy to raise the temperature of the air to a set point. But you were on low heat soit should have run OK.

[COLOR="Blue"]I uploaded 3 photos[/COLOR]
This was very helpful. I just wish I had seen something obvious to help resolve this problem.

[COLOR="Blue"](3) Exhaust blower wheel ineffective at pushing air into the exhaust pipe.[/COLOR]
It does look like the blower wheel has a lot of crud in it.
The white stuff in the picture you gave.
I would remove the metal face plate and clean it out.
May even be a good idea to remove the blower wheel from the motor.
I have never removed a blower wheel from a reversing motor.
It looks like it may have a locking nut on the end of the motor shaft and then the wheel screws onto the shaft. On normal units the blower screws on the shaft by a reverse thread. There is no locking nut because the blower rotation direction always tightens the wheel. I imagine the nut is there to lock it as when this motor reverses it would try to loosen the wheel.
On most motors you can place a wrench or vice grips on the pulley end (has two flat sides) to hold the motor shaft and then undo the blower wheel.
One thing to note is that on one direction motors often the blower wheel seizes onto the shaft and needs to be destroyed to get it off. I would not go this far in your case. If it does not come off the I would just clean it as best you can.
I do not know what this white stuff is. It could be residue from fabric softener so I would also check your filter screen. fabric softener (especially the sheets can coat the screen and then it has to be washed with soap and water to get it clean.

[COLOR="Blue"] is if it's somehow migrated out of position inside the exhaust blower housing. But it's bolted to the motor which seems to be in its proper position, so is that possible?[/COLOR]
I do not think it is possible for it to move when everything is bolted down. Also if it did move you would probably hear it as it would rub on the blower housing.
This is a long shot but try holding the motor shaft and turning the blower wheel. There is a remote possibility that the blower wheel is partially stripped so that when there is no resistance to air flow (empty) it turns OK but when you add clothes (resistance to air flow) it slips on the shaft.

[COLOR="Blue"]There may be a leak around the felt seals attached to the inside of the front panel, that fit inside the rim of the drum. The upper felt (which has 3 white nylon glides on which the rim of the drum rests) is much thicker than the lower felt--you can see that in one of the photos--so I assume the difference in thickness causes at least a minor leak. But it ran okay like that for years.[/COLOR]
Have you had what looks like rust marks or holes in clothes. This is an indication that they are getting between the frame and drum due to a mounting problem.
This and the rear support bearing is a possibility. The reason I say this is that when you put clothes in the unit you add weight to the drum which could open up an air leak. The glides do look fairly worn. I would also check the lower seal to see it it has even wear etc.
Check you rear bearing support for wear. If you have to re-lube it be sure to use a high temperature grease.

[COLOR="Blue"]I doubt there's a leak at the foam rubber seal where the duct below the lint trap meets the exhaust blower housing, because it looks okay to me. (It's shown in one of the photos.) I suppose I could try to test it by coating it with vaseline and checking whether the vaseline residue it leaves on the exhaust housing makes a solid circle.[/COLOR]
I also doubt this is the problem because adding clothes should not effect this seal.

[COLOR="Blue"]Do you have any ideas about the possible causes of the overheating, other than disconnecting temporarily from the wall vent? I'm not sure I'll be able to reattach to the wall vent if I disconnect it, since I can reach the back of the dryer with only one hand and no eyes.[/COLOR]
Your test seems to show that the vent system is OK re: it ran OK on high heat with no clothes in it. If it was a vent problem it should have blown the fuse when you ran the high heat test.