We will not be able to use even high-Tc superconductors (highest claim to date around 250K), because that’s still pretty chilly in an environment where you want to pump out heat generated. There is a discussion on Talk-Polywell with Johan Prins who claims to have obtained a much much higher Tc with his own diamond based process and theory. But still that might be doubtable.
So there is something called ultraconductors based on polymers which should have several magnitudes more conductivity than copper. Yes, polymers are insulator, but they claim with films that’s different.
Maybe overall it’s similar to graphene.