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.
You can transfer heat from the AI chips to the radiators however way you want (conduction, convection(using a coolant)). But that’s inside the closed system.
Transfering heat from the closed system to the heat sink (deep space looking from the permanent shadow regions of the moon) will only work with radiative cooling. The limiting factor is still how much heat can be *radiated* into deep black space. That was my point.