Space in itself has no temperature. It does have some background radiation, and thus you can measure its temperature (pretty cold at something slightly over absolute zero).

Here's the thing though. There's very little matter even in low earth orbit, so you can't use matter to transfer heat, as you would do on Earth (conduction and convection are out). That leaves only radiation, which requires a pretty large surface area. Try placing a computer on vacuum even on Earth and report back how the temperature looks like.

So no. Getting rid of heat is a big issue over there. Even in the shade.