Heat pumps need energy to operate.
Hence at low temperatures the best combo is electricity+heat-pump. So cryptomining+heat-pump is exactly the same, minus the e-waste.
Don't heat pumps work like a fridge/AC but backwards? That is, compressing the air inside to generate heat, then decompressing it outside where it gets extremely cold and is warmed up by the relatively hotter outside air?
If so I fail to see how cryptomining features in there.
You're right, the compression step is mechanical. Heat pumps are the most carbon efficient after ~0°C.
So in most parts of the globe electrical heat-pumps are the most environment-friendly. Thanks I Edited my first comment.