I had the same problem a few years ago. I was not really looking for a precision thermostat but rather a backup system in case my home AC ever went out while I was away, or if the oil heater heated up the room more than expected. The thermostats on most window AC systems only control the temperature of the air that is blown out (they often don't even give you the actual temperature range) but will continue to blow air even if the air is already cooler than what you have the thermostat set to. This is the case with my unit. Here is a picture of my window AC.

I searched around all over the place and ended up finding my solution at a greenhouse supply shop (online). Unfortunately I do not have the URL any longer. You should be able to find a few places selling them by going to a search engine and entering in greenhouse and thermostat. They are not cheap (around $50 to $75). Here is mine:

The way it works is you plug it into an electical outlet, set the temperature on the thermostat ( I have mine set to about 88F so if my AC goes out, the reptiles shouldnt get any hotter than this) and then you plug your window AC into the electrical plug on the thermostat. If the temperature rises above 88F (or whatever you set the thermostat to), then the thermostat provides electricity to the window AC unit and it turns on and starts cooling the room. Here is how you plug it in (sorry for the blurry pics, I put this together pretty quickly for you):

Hopefully this helps you. I know it has worked well so far and definitely gives me peace of mind.
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