Latency becomes high but you send large batches of work.
Probably not at all economical compared to anywhere on Earth but the physics work better than orbit where you need giant heat sinks.
https://pmc.ncbi.nlm.nih.gov/articles/PMC9646997/ ("Thermophysical properties of the regolith on the lunar far side revealed by the in situ temperature probing of the Chang’E-4 mission" (2022))
https://www.engineeringtoolbox.com/thermal-conductivity-d_42...
(Imagine, for entertainment purposes, what would happen if you wrapped a running server rack in a giant ball of rock-wool insulation, 50 meters in radius).
Only way to dissipate large amounts of heat on the moon is with sky-facing radiators.