I would think that orbital data center would have some real problems with heat dissipation, since you can only cool via radiation in space. Terrestrial data centers already have a problem with heat, and they can cool via convection (which is what is ultimately going to cool those air-conditioners). And then there is the cost of lifting thousands of soon to be obsolete computers into orbit...

I'm not a scientist, but isn't it super cold in space, just above absolute zero? If you can keep the (direct and hot) sunlight off the boxes with reflectors, I'd think the ambient temperature would be far lower than anything attainable by earth-bound datacenter cooling systems, so therefore radiation would be a most excellent cooling system. In fact, you might have the opposite problem, and have to figure out how to reliably prevent the boxes from freezing when not exposed to sunlight.