Inside of habitations covered with several feet of insulating regolith, the problem will not be the hot Sun by day or the super cold temperatures of the lunar night. Heat build up within habitations caused by everything from human body heat to cook stoves and ovens, electronics, electric motors and metal casting furnaces will be the problem. Air conditioning will be necessary. Air conditioners could dump excess heat into space with radiators out-vac like the one pictured above.
Furnace jackets and molds might also be cooled by systems of pipes, compressors, pumps, valves and space radiators. Oxygen and silane could be liquefied too. LIquefying hydrogen and helium would be much more difficult with four stage cooling systems. Perhaps hydrogen and helium could be stored in carbon nanotubes. Presently, it is possible to store hydrogen in metal hydrides consisting of magnesium hydride or FeTi alloy hydride powder. Hydrides are heavy but very dense and consume very little storage volume, so they are good for stationary applications. See: Lunar Gas Storage
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