Vacuum is only one of the best insulators around if you're near other warm things, I'm afraid. Out in space the dominant form of heat exchange is the Stefan-Boltzmann law, which says that if you have a half-acre of total surface area on your moon-base, and it's at 300 kelvin, then you need to supply about a megawatt to keep it warm.
It's not an insurmountable problem, of course -- Tesla just announced a battery for Australia at 129 MW-hrs, which would sustain the thing for 5 days, which is not enough but it's only a half-order of magnitude off. (I'm also not considering something like nuclear heating; it's not uncommon to have a 1000-megawatt nuclear reactor in the US and that's just the power output, not the heat -- so it's not a terribly bad way to go if you can shield the rest of the base from it. The only hazard with that is one recently discussed by John Oliver on his show, firing nuclear things into space is heavily, heavily complicated by the nowhere-near-close-enough-to-zero failure rate of launch rockets and the insanely-scary-cost of distributing a bunch of reactor-grade nuclear fuel into the atmosphere.)