Had the same idea back in the 90s and made a test pile. It could be done, self pumping, with a passive thermosiphon setup, leading to a radiator where you want ther heat, then it dumps back down into the pile.
Changing it out yearly might be a chore, because your heat pickuop hose has to be really embedded in there, but the idea has merit. I was going to make one here but the big chipper broke, and it is above my pay grade to deal with it. If/when the boss gets it fixed I will try one, or the greenhouse primarily to start with.
We have three big composting barns here, for chicken litter, they periodically catch fire. Then it is payloader and skid steer action to get the burning stuff outside where it can be put out.Theres a fine line you dont want to cross between real high temp proper composting and catching on fire. Main thing to watch out for is excess moisture in whatever you are composting.