>> more efficient to just burn the fossil fuels on site.

You forget exactly how efficient a coal-fired powerplant actually is. Love or hate them, they have 100+ years of technological innovation to squeeze every watt out of coal. Your fireplace at home is not nearly as efficient. So an electric heater powered by the grid is almost certainly more efficient than burning your own coal at home in an inefficient stove.

A good oil-burning heater has over 90% efficiency. Even no so good and cheap one can get over 70%. The best industrial electricity-generating plants that runs on oil has efficiency bellow 60%.

Does that oil-burning heater need oxygen? If it does then it needs ventilation, air movement in/out of the house, pushing that 90% efficiency number way down.

Tech connections has what you're looking for: https://youtu.be/lBVvnDfW2Xo

Efficiency wise, the comparison between a heat pump and a furnace depends on the outside temperature. Heat pumps lose their efficiency for high ∆T, so for winter in a Russia, a furnace is likely the better option

90% is overtall efficiency including losses due to ventilation. Such system with its heat exchangers is not cheap, but long term it pays off compared with less advanced heater.

You’re ignoring heat pump technology, which can result in greater overall efficiency than converting energy directly to heat.

The parent comment already addresses heat pumps. I'm explaining that there is virtually 0 practical use case for using mining to heat people's homes.

that assumes the use/utility of the computation is 0. We can all debate if that's true or not about cryptomining.

One day we may heat our homes with distributed computing like BOINC.

Consider the house that marginally has electrical resistive wall heaters (Like the bay area) and an excess of spare computers sitting around (also like the bay area) ... It's marginally better for the house nerd to leave their PCs on using BOINC than run the wall heater.

If by mining, you mean cryptocurrency creation, the utility is effectively 0. You can achieve the same utility if a cryptocurrency simply credited all new coins to my wallet. If by mining, you mean validating transactions, then that's something you have to do all year round, even if it's warm. That makes about as much sense as asking VISA to send me a rack that does computations for them only when my home is under 20 C.

yes, which is why the rest of my comment was about BOINC

Burning fossil fuels on-site means transporting fossil fuels to people's houses. Natural gas has a GWP which is 21 times that of CO2, and residential natural gas distribution systems are responsible for massive emissions just due to the leaks.

Unless you assume CCS for the fossil plant, which is not a setup that would work well for a typical residential forced-induction gas-fired central hot water heater (combined with passive radiators in rooms or underfloor heating).