(Note: the following is one of various posts that were copied here from the Moonwards.com forum for the sake of preserving the early days of the project. It was originally posted there on Feb 11th, 2016.)
I suffer from a severe rabbit-in-headlights reaction when i open the Lunar Sourcebook. Yes, i know it is a venerable tome that contains about everything i need. But it is also extremely detailed and dense and designed for people who are trained in the field. David Kring's Powerpoint summary of its information on the nature of the regolith is much more my speed. I was musing over it again this morning. It tells a tale of regolith density at depths over a meter that (once again) is not the idea i had. There are so many things to know, you see, and though i've scanned a lot of material, some things take a lot longer to register clearly than others.
So, alright, as we can see on slide 22 of that presentation, below the first foot of regolith, relative density rises to over 90 percent. And on slide 27 we see that there it conducts heat as well as porcelain does. So forget what i said about it being a good insulator. It will suck up heat like crazy. However, we are still okay, in fact this could be regarded as a good thing - as long as you think more long term. Let us talk about heat islands.
Heat diffuses outwards in all directions based purely on the statistical likelihood of a particle with more kinetic energy striking one with less and thus transferring some of its energy in the collision. We experience that kinetic energy of molecules as heat (well, unless a very large number of them are moving in the same way at the same time). When you pour heat energy into a medium, the heat moves away more slowly the closer the temperature of the surrounding material is to the temperature at the heat source. So the longer heat is poured into the ground around the sunken hall we are building, the slower it will move away. At night the heat closest to the hall is just as likely to move towards it as away from it. When dawn arrives, heat starts pouring in again, and at first it will sink in to the ground faster than it did at sunset, because the ground is cooler than it was then.
The regolith deeper than 80 cm remains at a pretty constant temperature all day and all night. That temperature is about -20 degrees Celsius (-4 Farenheit). Once you expose that layer to the heat of the sun, it will start warming up for the first time in maybe a billion years. Then at night you want to limit heat loss with reflective insulation so that heat builds up. Thus we seek a recipe in which enough sunlight pours in during the day, into the right geometry of material, to create a heat island where the temperature stays reasonably close to something pleasant all the time. And we'd like to reach that temperature within a few years, so that people can arrive to a temperate clime. To get that done we are talking about dumping in a lot of heat, but it should be possible to achieve a desirable balance in a few years with a good design and possibly a few tweaks.
On Earth this approach to temperature control has probably best been explored as Passive Annual Heat Storage. The rule of thumb in that method is that if you thermally isolate a volume of dry soil extending 6 m from an underground home and heat it to the desired temperature, the temperature in the home will stay within a degree or two of that year-round using only the passive heat of the sun, through south-facing windows in a normal-looking house, other than that the rest of it is buried under a thick layer of soil. Beyond that 6 m point the temperature slowly falls to the annual average, which on Earth in mid-latitudes is 5 or 6 Celsius. If you look at the 'Look Inside' preview of the book at the Amazon link above, there is a case study where such a home's earthen thermal store reached a good temperature within 2 years, and was close after only a year.
On the Moon the temperature gradient we have to deal with is much steeper, -20 to 20 Celsius, 40 degrees instead of 15 or so. But the conditions for doing that are very favorable. Sun that averaged over time is twice as strong as what most places on Earth receive, the ability to control heat loss quite precisely and completely with just a few sheets of reflective foil.
My guess - and i say this with 68 arbitrary units more confidence than i've said other things - is that even the smallish sunken hall planned in Phase 1 can have a pleasant area of windows (or, you know, window-like objects) and be kept at a pleasant, even temperature using only reflective shutters. A set of them hooked up to a simple program that opens and closes them on some schedule would be enough, and at least a couple could always be open for that key view of the full Earth bounced into the hall from a mirror.