Could we use a constant stream of micro-asteroids as a heatsink?

i think so, next is Quantum right?

No, just you. Superconductors don’t get hot. There is 0 resistance in superconducting mediums. Theoretically you could manufacture a lot of the electricity conducting medium out of a superconductor. Even the cheapest kind will superconduct in space (because it’s so cold).

Radiation may be sufficient for the little heat that does get produced.