You still need fees or inflation because you can't force everyone to install a miner-heater. Some people will refuse. Some people will not upgrade it after 5 years. Some people will want to mine in another fork / altcoin.

So the fee/inflation is important to pay the additional cost of the miner-heater, and to encourage people to upgrade it.

I've seen a few similar projects before. For example https://techcrunch.com/2018/03/08/qarnot-unveils-a-cryptocur...

Right, I’m unclear where the incentive to run the node comes from if there is no payment for running it.

People might have an incentive to use mining rigs to heat their home but why not something that pays?

Why would you force anyone?

They are incentivized to buy a miner-heater because as long as it earns something, they are essentially just paying less for heating.