Question: At current electricity prices, what is the total cost of mining the complete 21 million bitcoins set?
All profitable miners would be using the most efficient hardware, in a location where electricity is cheapest.
Current mining is probably using on the order of ~30-50 MW. At 10 cents kw/h (low estimate), that's ~$100k/day. It also grows with the price of Bitcoin, so it has been growing rapidly recently.
In other words, you could mine the full set of bitcoins for virtually no electricity whatsoever if you could convince the world to abandon bitcoin mining completely, then just let a single old, slow, cheap miner run in the corner for the next 100+ years. Or you could use as much electricity as you wanted on the project by throwing more and more computational resources at it.
(I don't actually do this because I don't have a desktop computer, and it's unclear if building one at this point will pay for itself before custom integrated circuits push the bitcoin difficulty so high that GPUs become worthless)
Of course, energy has to be expended to move heat around, and there are inefficiencies. But with real-world equipment and common cold-but-not-too-cold temperatures, a single unit of electricity can be used to move several times as much heat as it would produce if you just converted it to heat directly.
A computer is as efficient as anything when it comes to converting electricity to heat. Heat pumps win because they're ultimately playing a different game.
But, thanks for clarifying.