depends on the type of thermostat you buy. The snake forums tend to have alot more information about the various types of thermostats available, as they are used in rack systems to control heat.
In your new home if you want the room controlled by a thermostat more than the cage itself..most AC's have a built in thermostat and will turn off (some will have the fans continue to run though, to circulate air...check the manual that came with the AC unit). Central Air could be a bit tricky as it tends to go by the ambient temperature wherever sensor is placed upon installation (no clue where this is by default...whether it is on the AC controller/thermostat or elsewhere)
I suppose you can plug an AC unit into a thermostat to turn it on or off if the temperature reaches a certain high in the room, then shut it off when its under another temperature (say turn on AC at 85F, turn it off at 75F)
The way you have it now, I would adjust how cold your AC gets the room so it cools only to 75F.
Another thing to keep in mind is when you are in your new place, the room you have your reptiles may not have the same issue with getting too hot due to facing east. Or try and select a room that is north or south facing..and/or has little to no windows. Or just put everything in a basement room. (if it gets really cold in the basement (ie below 60F), a ceramic heater could be used to heat the room (providing the basement is finished and not just one big open area the same size as the main floor (cost much more to heat a large space than a small..though you could always build a reptile room in the basement if it is open) When heating the room, I wouldn't heat it more than 70F. Let the lights heat the rest of the cage, a 100watt bulb takes less power than a 6000 watt space heater.
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PHLdyPayne