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.
Like geothermal cooling, kinda. Possibly a passive solution could work somewhat?
It'll be a temporary solution, the regolith will heat up eventually, but maybe it'll work for long enough?