As to the cost, you wouldn't have to have the newest and best out there - I bet if you made huge amounts of small dies on, say, an older, cheap process and chained them together in some way you could make quite decent economy out of it. I'd think routing a network cable to every heating element you have would be a problem though.
Also, you'd need to "chain the cores together" in such a way that 1) they can take quite a bit of punishment, such as playing kids throwing their schoolbooks all over them and 2) they will degrade gracefully as the cores break, and 3) they'll have the bandwidth to shuttle the data back and forth, preferably without an external controller allocating the work, and 4) they will still have enough computing power to actually matter, and 5) they'll last for a long time and can take extreme heat variations when people don't need their heater and put it in the attic.
Solve those problems, and you may just have something.