There's two cooling problems, pulling heat off the wafer (water cooled loop or immersion cooling, this is easy) and dumping the heat somewhere. The second part is why the place being cool matters, I imagine a big radiator on the roof. Could also dump the heat into a river if it's chill.
Let's build it on the crest of a lunar crater. Wafers on the shade side and solar panels on the sunny one. “Just” add some $Bs to send the stuff up in the space.
Shaded or not, cooling is actually a problem in space because radiating heat in to a "vacuum" is hard. Even a warm atmosphere is easier to transfer heat to than almost nothing.
Now a ground source heat pump could be interesting as long as it's not too hard to drill for the plumbing.
There's two cooling problems, pulling heat off the wafer (water cooled loop or immersion cooling, this is easy) and dumping the heat somewhere. The second part is why the place being cool matters, I imagine a big radiator on the roof. Could also dump the heat into a river if it's chill.