I think the hardest part will be getting it to check for temperature change often enough, but also remember when it has nudged and not re-nudge too soon, or worse, over and over.
This helper sensor SHOULD (I hope) be degrees of change per minute, +/-.
My best guess is a 5° change in the room warrants a nudge.
I also want a cut off. If the room is over X°, just turn it off.