Assuming Folding@Home has some sort of API or if it can be started and stopped from the command line, it should be fairly straightforward with an Arduino a simple script.

It already exists. There is a company that sells a space heater that mines crypto currency. You get like 50% or the profits which sucks, but you at least recoup a bit of the cost of the electricity to run the heater.

I think we should try to heat ourselves with computing as much as we can since the side effect of computing is heat generation (and minor RF losses). How cool would it be to make a large supercomputer out of millions of homes heating up in the winter?