Any 2 wire thermostat will work. This one offered by APP is a quality one that should last for many years. Comes with instructions and is made by White Rodgers a hallmark company in HVAC parts. It costs a bit more than an el cheapo home store type one but you gets what you pay for. Instructions included. A few things you may want to do before turning on the thermostat. Check the gas valve for the amp draw. .2,.3,.4 etc. Set the heat anticipator to the amp draw of the gas valve. Why? This is so the heat will shut down a hair earlier and not overshoot the comfort zone and run you out the house. Then when it shuts down it waits till freezing to cut back on. Most of the thermostats are pre set but it never hurts to check. Never touch the 2 wires together at the gas valve to see if you have power. Doing so will fry the heat anticipator and you will need to buy another one.

Here is a few notes I wrote down concerning these fine wall heaters:
Their are a couple different versions of these. The originals had no fan and used millivolt wall themostats. The fan driven ones use the same thermostat. The millivolt gas valve relys on the voltage from the thermophile to control the whole operation. Yours however does not use a thermophile( a thermophile cost $75) Yours uses a $7 thermocouple so that tells me your heater works with a 24 volt transformer. Like I was saying the Williams wall heater uses low voltage thermostat mounted on wall. If that thermostat has no continuity get another one. The heater uses a 120 to 24 volt ac transformer to power that gas operator on the combination gas valve. It is called a combination gas valve because it combines a gas operator( to open the burner gas thermistatically) and a pressure regulator to bring down the meter pressure to specific pressure to allow for the rest of the gas appliances in the house to function properly. The transformer is located up near the top of heater where the power cord comes in. If it is bad then the heat will not come on. Remove the 2 wires on the gas valve operator and check them for 24 volts output. Never touch the 2 wires together to check for power as this will fry the heat anticipator on the wall thermostat and ruin it. Check the 2 terminals on the gas valve for continuity. If they are open the gas valve will not work(the pilot will, but not the main gas). The gas valve has a thermocouple whichs holds open the gas when the pilot is lit. The thermocouple has a ceramic fuse mounted in series which kills the thermocouple and shuts down the gas, when the heater gets too hot. The burner must be wire brushed cleaned well to prevent uneven combustion. The heat exchanger must be clean of cobwebs and rust. The chimney stack must be clear. If not, the heater fuse will shut down. The burner will fire off but the fan does not come on right away. The fan klixon mounted midways up the heat exchanger under the front cover will turn the fan on as soon as the heat exchanger is properly warmed. Another 3 wire klixon controls high and low speeds. A third one is a high limit which shuts down the heater if that fan won't come on. The heater is pretty easy to work on. The burner assembly is removable for bench testing and repairs. The gas valve will need replacing sooner or later and you can damage the burner if you are not careful. I put the valve in a vice and turn the burner near where it screws into the valve. The fan blade will tend to rattle and this can be fixed by peening the hub. I remove the fan blade and set it on a 1/2 inch shaft, using a ball peen hammer and blount nose chisel. I dimple the hub all around the shaft to tighten it up. Hey it saves 50 bucks. I also oil the motor with Hi temp oil. I use zoom spout turbine oil.
The pilot on these heaters is mounted on the cast iron burner so that when heat is called for the flame will quickly ignite the burner.
To light this heater: Move the knob to the "PILOT" position. Press down on the gas knob and light the pilot. Hold down on the button until the pilot stays lit with the button released. Move the knob to the "ON" position. If the wall thermostat is in the on position then the burner should light off. After a minute or so the fan should kick in. When the wall thermostat is satisfied the burner will shut down but the fan will continue to blow until the heat in the exchanger drops