“can anyone explain why a t-stat is different in halacha then a timer.”
“My question was : what is the difference between a thermostat and a timer. Both are going on and off at different intervals. ”
Rav Moshe explains it very well in the Responsum posted by Da’as (Thanks DY!). And as DY explained it , it all depends if the act of the Malacha was already done prior to Shabbos. The very function of a Timer is that the Melacha act should be done at a certain time, which is on Shabbos.
I don’t know which part a thermostat is comparable. It is not the “on” and “off” that is the issue, on that you have the Nemukei Yosef’s sevarah, that it all depends if the “act” has already been done, and as for a Timer , “setting up” is not considered any act. Whereas a fridge the turning it “on” for the first time is considered your “act” . It is no different then Bishul, that putting it on the fire is all that counts, even though that it is being cooked at a later point in Shabbos, as long as you did it before Shabbos it is fine.