Somewhat harder but not a lot. Most heat loss occurs via (electromagnetic) radiation. Does not require a medium like air or water. Only 15% or so is via convection (requires a surrounding fluid).
Listen, the heat-generating computing elements on the moon are going to be sealed/packaged and not directly exposed to the heat-sucking black of space.
There’s going to have to be some sort of recirculating fluid flow to get the heat out of the processor/component enclosure to where radiative cooling is available.
Prior comment maybe incomplete: Conductive heat transfer from processors to space-exposed radiating metal plates seems like it may not scale. Hence maybe also using forced gas or liquid flow to meet cooling requirements.