Though in all fairness that isn't much of a problem for a superconductor - no resistance, no waste heat when power runs through it.

The main problem would be the waste heat from the rest of the system rather than the superconductor itself, so maintaining a superconductor cool is more a thermal insulation problem and the near vacuum of space actually helps in doing it because it removes the heat transmission from the hotter parts of the system to the superconductor via the environment (though, of course, it still happens via the solid parts in contact with it, so the thermal insulation is needed there)