That doesn't sound right to me. If there's no air, then only black body radiation can be used to cool the data center. That means a massive radiator, a lot larger than a heat-to-air radiator+fan used on earth.
For all the heroics needed to establish this ok the moon, the efforts and costs are much less back home.
Oh, we're overpopulated? Buy some single-family homes, buy out the government, and upzone it into apartments. You're still cheaper than space flight and with a shorter commute to work than Rapture