At those temperatures you'd need something multi-stage with liquid metals, which is going to be a nightmare to engineer - you'd need some way of preheating it t

At those temperatures you'd need something multi-stage with liquid metals, which is going to be a nightmare to engineer - you'd need some way of preheating it to melt it so you could turn it on in the first place, for example. And heat pumps are much less efficient at high temperature differentials, as would be the case here.