No. The value of a PoW coin is based on the wasted electricity.
If mining does something useful (like heating) for a large fraction of the miners the mining difficulty will go up to adapt to such change, requiring additional mining.
At the end of the amount of wasted electricity will remain the same.
I have a degree in EE.
The wasted electricity is in additional heat that you don't want in your home and you have to vent.
Suppose millions of people could replace resistance heaters with mining rigs that cost exactly the same and consume exactly the same amount of energy every day.
Such people would be running the miners ever if the financial gain is very close to zero, because they were already using the same amount of electricity for heating.
That means they would push the mining difficulty up. But, if the demand for coin remains the same, other people will run mining rigs that releases increasing amount of heat in the environment.
You just pushed the amount of wasted heat from one place to another.
Regarding heating things with electricity, a heat pump is way more efficient than resistance/mining heating because is moving existing heat from one place to another.
Define "cold". Mitsubishi units have 100% of capacity at 23F/-5C and 75% capacity at -13F/-25C:
* https://www.mitsubishicomfort.com/benefits/hyper-heating
They're used in Alaska:
* https://www.nrel.gov/news/features/2021/even-in-frigid-tempe...
Fujitsu says -15F/-25C as well:
* https://www.fujitsugeneral.com/us/residential/technology/xlt...
At the 'break down point' an air source heat pump (HP) is no worse than a baseboard heater: in both cases the COP is basically 1.0. So you might as well go with the HP as it'll be more efficient for probably the majority of the year.
You can get gas furnaces that are 'dual fuel': they'll run the HP refrigerant through the exchange and circulate the conditioned air, and once it's "too cold" switch to gas.
If you're going to buy a only-cooling AC unit, then spending a little more on a heat-cool HP is probably a smart idea. There's a payback period, and it depends on the price of your electricity and fossil fuel (NG, propane).
(In other places and to a larger extent pop culture, "geothermal" refers to tapping into actual heat sources underground.)
They simply periodically pump a bit of heat back out to keep the exchanger free of ice.
You'll periodically need a backup source of heat, but most of the time you'll be fine with the heat pump alone.
The approximation for electrical use in heating is using heaters that can output roughly 10 watts per square foot of your house. 12-13 if your house is poorly insulated.
At full power, that means that a 1,600 sqft house requires 16 kW of electricity. At a cost of 13¢ per kWH, that's about $2.05 for that 16kW of electricity. Of course, no residential house will ever realistically have 16kW available to it, nor would heating ever require a 100% duty cycle. But this is for comparative purposes.
The equivalent amount of gas power would require about 54,000 BTUs from a gas furnace (about 3.4 BTUs per watt). One cubic foot of natural gas provides 1,032 BTUs which means that generating 54,000 BTUs of heat requires about 52 cubic feet of gas (we'll round that up to 65 to account for inefficiencies of a furnace; top end furnaces are in the 80-80% efficiency range). 100 cubic feet of natural gas costs about $0.48, so the cost for natural gas would be around 30¢
Again, neither will (nor could, nor should) run constantly, but it's a sobering comparison.
EDIT: Comparisons were hours vs. seconds; fixed.
That's not necessarily always the case. There's a threshold where the delta between the outside ambient temperature and desired indoor temperature is too large, it becomes more efficient to use something like resistive heating rather than a heat-pump
This also doesn’t address the wasted materials and labor used to make the chips.