The moon is a near vacuum, so aerogel is the wrong approach. The main form of heat loss is radiative, and the way to reduce radiative loss is with many layers

The moon is a near vacuum, so aerogel is the wrong approach. The main form of heat loss is radiative, and the way to reduce radiative loss is with many layers of shiny things. This works like the superinsulation between layers of a Dewar flask. It could be literally a layered structure or a filling of shiny fluffy stuff inside something else. This will dramatically outperform mineral wool or really anything practical on Earth. All this insulation goes on the outside, vacuum side of whatever pressure vessel people live in. To the extent the lunar atmosphere is dense enough to cause meaningful conductive loss, one could pump a better vacuum inside the insulation. The pressure difference between this high vacuum and the lunar atmosphere would be low, so the mechanical strength needed for whatever container holds it would be corresponding low. (This seems very unlikely to be a problem at all. The moon’s atmosphere has an extremely low pressure. Offgassing from the insulation seems like a bigger concern.