[throwaway189262]

If building stuff is an option, 14 days might not be so bad.

You can store heat as heat, cooling as ice. They already need a huge water supply, why not freeze it for cooling?

Another option, unique to the moon. Why not just run wires to the sunny side. You could probably use uninsulated wire at a pretty high voltage. Nothing to disturb it or get electrocuted up there. You could do like 5 kilovolt on a hair thin wire to get usable amount of power across the moon with maybe 200lb of it