

The energy requirements for keeping a magnet out of the sun at all times, is probably considerably less than powering a conventional electromagnet for the equivalent duration.
We’ve already achieved this on the extreme end via the new horizons probe, I’m not sure what all the fuss is about.
Superconducting magnets don’t heat up naturally, not without breaking. All we’d need to do, is engineer an isolated environment for the magnet, and there’ll be no chance of it heating up, except maybe for an intense solar storm overwhelming it’s magnetic shield.
Unlike earth, where there are multiple potential sources of heat, in space the only one of note is the sun. So yes, you can’t remove heat via conduction or convection, but that also means that you can’t gain heat from it. If anything, that simplifies the design.