Furnace with a powerful computer system providing the heat. Will use compute cycles for scientific research or other social or personal purposes, running things like BOINC, Folding at Home, crypto mining, or rented “cloud” usage. Fans or liquid cooling systems will carry heat to a traditional forced air or water boiler system to distribute the heat throughout the home / building. System will increase or decrease CPU usage based on thermostatic control. Computer system will have max thermal dissipation capacity equivalent to a standard furnace for the same building, which will make for a lot of computing power. 18 kilowatts would be expected from a furnace in a 2400 square foot house, which is a huge computer.
Could be hybrid with another heating source such as gas or regular electric elements if that amount of computing power would make the furnace too expensive.
Will have wifi connectivity and require a wifi connection to operate above examples. Will be able to fall back to generic high-cpu local computations if needed or preferred.
Likely a Linux system or cluster, with a standard distro to get automatic security updates, but with a furnace company software repo to manage the heating part and user interface. Furnace company will likely offer a user interface to pick one or more options for what the CPU time will be used for. Any crypto / CPU rental options could be done as a service through the company where proceeds are paid to the furnace owner, presumably with a cut taken by the company. Ideally, the OS would be accessible by the owner via SSH, where the owner could install and run any software on their own to have it do whatever they want.