I don't think it will matter much though. Whether you have to remove input power as heat or expend power to cool likely won't make a whole lot of difference. Just that the delta-t will be a lot larger and so it may actually cost more to keep that ultra-cool machine ultra-cool.

Maybe future data-centers will be used to pre-heat the water that goes into the turbines that power the electricity plant, in some kind of perverse version of a perpetuum mobile.

You'd need to make up for the difference lost on each cycle with extra fuel.