I think for the work, it'd make more sense to haul around undecayed wood to burn in a wood heater. I imagine an underfloor
compost arrangement would give off more heat, and here you could possibly toss kitchen scraps or other household wastes (shit, etc.). The difficulty would be access, both for input and then clearing out later. I'd hate to crawl under my house and scoop out decayed matter.
Another consideration that comes to mind is moisture. Floors tend to have vapor barriers below them (at least in my humid/wet climate) to prevent rot. They're also often insulated (to prevent heat loss). These would make for other other obstacles to using such a system in a conventional house. But if you're doing something unconventional/natural perhaps you could find biological processes to add heat to your house.