Not a silly question at all. Firstly, heat pumps do not need to extract heat from the ground, they can also extract it from the air or a body of water. The heat moved from outside to inside a building will always leak out eventually, returning to the environment. In the case of air heat pumps this means there is very little change of local air temperature over any time scale.

You are right that extracting too much heat from the ground will make the ground around the exchanger too cold, which will make the process less efficient and have negative environmental effects, which means it is illegal in many places. Smaller systems like for homes are usually very shallow and will regain enough heat from the air and sun over the course of the year. Larger systems can be problematic. The common solution to this is to use the ground as a thermal battery (or install a thermal battery in the ground, using it for insulation). Then you can use your heat pump to extract heat in the cold season and in the warm season you can cool the building and move that heat back underground. This has the extra benefit of being even more efficient, since you are basically just trading heat and cold from season to season.

I think this is a really good way to put it into perspective, because the units we use for temperature are very misleading on this front:

Where I live, the outside temperature goes from -40C to +40C at the extremes (though those are rare and the 'normal maxes' are more like -30 to +30). In F that's -40 to +104F.

But in kelvin, which actually measures the amount of energy in the air, that's 233K to 313K. It's not a small difference in the amount of energy, but neither number is anywhere close to zero.

It's a common meme with heat pumps that they "stop working under X temp" because it's too cold, but the actual, immediately practical issue is moisture. Ice is a great insulator, so when the outside part of your heat pump is covered with ice it no longer works well. Presumably the same might be true of ground source heat pumps and frost, though I know less about that. Obviously there are other factors like the efficiency and operating range of the coolant used and such, but you hit this moisture barrier before those.

There are ways around that (I installed an air source heat pump this year and it runs in reverse (ie. as an air conditioner) periodically to defrost the outside part. I've used it successfully to heat my home down to about -20 outside before it no longer spends any real time in heating mode. It wasn't cheap though, and is almost certainly not cost-effective even over a very long time period. That's not my priority though.

> Presumably the same might be true of ground source heat pumps and frost, though I know less about that.

I looked into this, since I'm getting an air-to-water heat pump installed next month, and considered a ground heat pump. Ground heat pumps require a large area of pipes, roughly 3x the area of the house. Less than that, and I was told that I'd risk creating permafrost around the pipes, greatly reducing the efficiency of the pump.

Regarding cost, my heat pump will replace a gas heater, and should actually cut my yearly expenses to almost 1/3. If that is actually how things are going to work out (and assuming the electricity price surges in Europe are temporary) then it'll pay itself back in 8-10 years. Granted, I live in Denmark where most of the price of gas and electricity is environment taxes, and those are cut for the electricity that is spent by a heat pump, thus making it more cost effective than if those taxes weren't there.

Most of the cost for me was really a "no one here does it yet tax" on the unit itself, along with an "everything is much more expensive in canada tax" tbh. If I were in the US the unit would have been half the cost and it'd probably be cost effective on a reasonable timeline, esp. if carbon taxes increase over the next ten years as currently scheduled.

Right now though the cost to heat my house with gas and the cost to heat it with the heat pump at the marginal temperatures is about the same. I still have an operational and relatively new gas water heater though or I'd be looking into turning off the gas for 2/3 of the year and that would save a lot of money since there's a lot of fixed costs on my bill for even having gas at all.

Ground source heat pumps with shallow heat collection coils extract heat stored by the sun during the previous warm season.

With deeper boreholes you're extracting heat from radioactivity decay.

In both cases the rate at which you can extract that heat depends in the heat transfer rate in the ground around the coils/boreholes.