It would be way hotter in general. Conductive cooling requires a medium to transfer heat. In a vacuum, you only have radiation, which doesn't cool quickly enough for a shit ton of processors. In the sun, it would be worse, but they would need cooling even in the shade.

So you’d need to be able to radiate more heat away than you absorb from the sun (and generate from computing). You can reduce sun absorption by being more reflective. For the heat you do absorb and generate, you’ll need to concentrate the heat from all the systems into a radiator that gets very hot. The hotter something is the more it’ll radiate away. It’s hardly a simple design but it’s really the only option.