"Could a solar sail above the surface cool a region that is suffiently large to cool the underground to the single digit kelvins. "How would this work? How does a solar sail cast a shadow on one spot long enough to cool anything significantly? You might have a huge sail and cast a shadow that drops temperatures by 200 K or something like that - during the day - but it's moving in orbit, it can't cool for long. If it's in a synchronous orbit - if such is possible at the Moon - the sun shines from a different direction all the time. If it's aligned with the sun vector, the moon rotates under it. You can't cast a shadow on the same spot for very long.