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Glad you solved your problem!

I should have asked this earlier, since you said your dryer's thermal fuse would blow after about 30 minutes: How dry did the loads get in 30 minutes? For the moment I'll assume the loads had completely dried, since you wrote that you discovered the dryer wasn't working when you tried to do the next load.

Once the load becomes dry or nearly dry, evaporative cooling stops cooling the load & drum & exhaust. At that point, the heat needs to be regulated. (Since the exhaust gets warmer then, the exhaust temperature can serve as the input signal to the regulation circuitry.) Overheating that occurs after the clothes are dry or nearly dry is likely due to an issue with the heat regulation circuitry. This appears to have been the case with your dryer since replacing the control board fixed it.

The regulation circuitry depends on the dryer model. My 17 years old dryer uses a thermostat (called the "control thermostat" or "cycling thermostat" to distinguish it from two other thermostats in the dryer) located in the exhaust flow, and a fabric temperature selection switch & network of resistors to set the bias temperature of the control thermostat. Newer higher tech models use a thermistor (a temperature-sensitive variable resistor) instead of a thermostat, plus other control circuitry, for more precise control over the temperature, and may also have a moisture sensing circuit for additional control.

When I monitor my dryer's temperature, I see the control thermostat begin to regulate the heat after about 45 minutes, when the load has become nearly dry. If your loads are nearly dry after only 30 minutes, I'm envious!

Rereading your earlier messages, I see that your dryer would heat up even with the fabric temperature control set to air fluff (which is supposed to turn off the heat). That was a major clue... sorry I missed it. (On my old dryer, that symptom would imply a short circuit somewhere in or close to the fabric temperature switch, because the switch in air fluff position is supposed to be open.)