ok to correct myself. Due to lack of much air, heat would only dissipate by Black body radiation.
One would need to calculate if that could cool down the chips efficiently.
You can radiate heat from the surface of the earth into space via the sky, but you don't lose much energy that way.
That's not quite true. Black body radiation is the only reason why earth does not heat up much more. It's the only factor with a negative radiative forcing.
Solar radiation is the only main incoming source of energy, and black body radiation the only outcome with almost the same magnitude (which is huuuuge btw)
The actual surface of the earth has the advantage of being able to use the whole surface of the earth.
On earth you can use things like fans and evaporative cooling. It's far superior to making huge space radiators, but nothing is free.