The problem is that the act of computation is generating heat, so you can't just insulate your superconducting CPU, you need a way to dissipate the heat it must generate (this applies to all irreversible computations). This is difficult, because the only way to dissipate heat in space is radiation (with conduction usually acting as a middleman), which is constrained by the surface area of your radiator.

So no, it probably wouldn't be any easier in space.

Ideally this server farm would attach to a giant rock somewhere in a stable orbit and drill heat exchange pipes deep into the rock, like how we do for geothermal energy here on earth but in reverse. This whole exercise would require a nuclear reactor to be feasible both economically and engineering wise.