I think the exhibition area is reserved for showing off stuff not asking for ideas/troubleshooting or anything, but I'm kind of new here so I could be wrong.
Sounds like your idea is very plausible but speaking to the thermostat might be difficult depending on what kind of thermostat it is.
you might have to pull buttons off of it and connect them to arduino pins to simulate button presses, or even connect a servo motor to a dial style thermostat to turn it appropriately.