Yeah, space is cold, but also you don't have access to large thermal masses with which to exchange heat, so the fact that space is cold does not help much.
In space the only option for cooling is large radiators. If you had a data center in space you'd need enormous radiators -- much larger than the data center itself.
(On Earth we can exchange heat with the environment, and the environment includes convection and the water cycle and ultimately can expel excess heat via high altitude condensation of water vapor where most of the heat released escapes to space. As well clouds can both block insolation as well as keep heat below trapped, but altogether between high altitude condensation and blocking insolation this is the mechanism by which Earth keeps its temperature as a random walk around the average that we enjoy.)