An entry came in on the website forum about the extreme temperature swings between day and night on the Moon, and the difficulty of keeping temperatures even because of this. The poster, Sam D, mentioned in another post how lava tubes help with this, and that is indeed one reason why the idea of just sealing one up and using it as a hab is popular. I haven’t ever properly explained why the habs we’ve designed will have very stable temperatures, so, now i am. (There is a different version of this on the forum more tailored to the asker, here i’m rearranging it a bit.)
If you have enough mass within the whole gallery space, then heat regulation is easy. Just make sure that enough heat leaves over the night to balance what came in during the day. That will mostly happen through the rock of the gallery floor and lower walls. If anything, the windows won’t be enough for that and very minimal radiators would need to run every now and then at night.
In the Gallery, the heat entering during the day is what comes through the light tubes, and the water dome at the bottom, which is a small fraction of the sunlight falling on the surface covering the Gallery. Each light tube would pass in about 27 kW of sunlight all day, and there are 76 in the current design. Note that this can be adjusted at any time - shift the angle of the Fresnel lens, and the amount of light coming in can be decreased to any fraction desired. But if that wasn’t done - and it would be far better not to because sunlight really feels good and makes plants grow - the whole set would pass almost exactly 2000 kW of sun in all day. The heat capacity of most rocks found on the Moon is 0.8 kJ/kgK, meaning that if that sun was all hitting 2.5 tons of it, it would heat up by one degree celsius every second. Alright, that does sound like a lot, and is the exact reason sun is going to be used to make the materials for the habs in the first place. But the Gallery is going to have a HUGE amount of thermal mass.
The image below is from Constraints on the depth and variability of the lunar regolith by Wilcox et al, and shows the estimated depth below which the Moon is pure rock. Because of our lack of data, this model could be off quite a bit, and also in the case of large craters like Lalande, the regolith at the very rim has been modeled as being twice as deep as it is in the surrounding landscape. Still, considering how far down the crater wall the Gallery extends, it stands to reason that a large portion will be cut out of solid rock (and that isn’t a problem). So how much thermal mass does it have? Well, for all intents and purposes, it is a cave. Oodles.
In fact it will take time to add enough heat to the structure to raise the thermal mass that affects the interior temperature enough to reach room temperature, and extra sunlight will need to be piped in for that exact purpose. (Using lava during the building process helps here.) The temperature below the surface of the Moon is about -20 degrees Celsius, so heat will be sucked up by the surrounding rock in giant quantities thanks to that gradient. No problemo. What needs to be done is to pour in enough heat that it sufficiently saturates the volume of rock that will interact with the gallery. There is a distance from the gallery walls at which the heat coming in during the two weeks of sunlight equals the heat seeping away through the rock over a lunar month. Fill the volume of rock closer than that with enough heat to keep the gallery at room temperature, and it will stay at that temperature, cooling only very slowly over the night, but heating up again an equal amount the next day. If heat stops entering it would cool only very slowly, it would be months before the residents were at risk. And why would heat stop entering? There is no weather on the Moon, as long as the lenses over the light tubes turn during the day like they are supposed to, the only variable in the strength of the sunlight is the sun - so we are talking about a difference of about 0.1% between solar maximum and solar minimum. The only thing here is that it might take so much heat to get the gallery to the proper temperature in the first place that it takes a long time to pour it all in there. If so, a simple trench cut in the rock can be used to tailor the amount of rock involved. Any void is going to be a vacuum, which is great insulation, even if it is only a centimeter wide. Line it with aluminum foil and that makes it even better. So you can limit the area through which heat is seeping away by almost any amount. There is a book that uses this concept for the design of houses that use no heating, but remain quite close to the same temperature all the time by balancing the sun that comes in the windows with the heat that seeps out of a mass of earth kept dry and insulated from surface temperature changes under a layer of insulation and plastic. It is called Passive Annual Heat Storage, by John Hait. The concept never really took off as there aren’t many people with enough space, the inclination and money to have one built, and in spots where it isn’t too hard to gather enough bone-dry earth, and keep it that dry until it has been properly emplaced and protected. However, in the examples that exist, temperatures fluctuate only by 1 degree Celsius or so through the whole year, even in places with harsh winters.
Heat moves towards cooler spots, but it moves ever more slowly the less the difference in temperature is - the less the heat gradient is. When there is a large heat gradient and a cycle of heating and cooling, like over a day on the Moon or over a year on the Earth, places underground that are far enough away from the where the heat is changing basically never change temperature. Between that point, and where the temperature is cycling up and down, how much the ground changes temperature over that cycle smoothly increases. On the Moon, the temperature difference between the ground and the habitats would be about 41 C or so, much greater than that difference on Earth, and heat would flow through the bedrock much more quickly than it does through dry soil on Earth. The distance to where heat fluctuation ceases would thus be much further, which is why creating narrow trenched to limit the volume involved would likely be necessary.
In the drawing, the pink is the powder regolith, through which heat moves very slowly so it basically functions as a layer of insulation. The grey is the bedrock layer, the red is the stored heat that keeps the hab’s temperature steady. Because the big temperature difference is always going to be between the lunar surface and the interior of the hab, heat will always move mostly either into or out of the hab through its openings - windows, light tubes, the occasional airlock, and a few small radiators. So the heat in the ground at night will move mostly towards the interior of the hab, as heat leaves through these openings. It will also seep away through the stone, but more slowly because it takes so long for changes within the hab to significantly increase the heat gradient around the edges of the volume containing all the heat. The surface area involved is much greater, though, so again, we come to the matter of creating trenches.
There are many possible options for layout of the trenches, this is just one. Mostly what the trenches do is create bottlenecks to outflow of heat so more of it stays closer to the hab. At the scale of the gallery, the vertical trenches are about 35 m long, the horizontal ones 10 m, and the diagonal ones about 15 m, since the gallery is about 32 m wide (and varies in depth). So, creating them isn’t a small thing, but fiber-optic cables coming from sets of concentrating mirrors will provide a great tool for the job that can melt rock very quickly. Since the gallery is on a slope, the molten rock created can be drained away simply by allowing it to flow away downhill. Do this correctly once, and down the centuries this space will never need more than very minimal heating or cooling, so it is worth it.
The light entering the sports hab is indirect light reflected off the ground outside for the first 11.5 Earth days of each Moon day. The surface of the Moon reflects very little sunlight. In Lalande, which is brighter than surrounding land, it probably reflects about 15% of the sun’s light. How much heat would pass through the windows at different times of day is a complex calculation far beyond me, but think of it this way - it would be less than the heat passing through such windows on Earth due to indirect sunlight bouncing off lawns and fields. For 2.5 Earth days before sunset progressively more of the windows would be hit by direct sun, mostly at an oblique angle, so that over the course of that time maybe a quarter of that sun would pass into the hab. Water is about the best thermal mass there is, so 3000 tons of it in the pool will heat up very little due to that amount of sun over the day. It would take about 12.5 billion watts to heat it up by 1 degree Celsius. Taking everything together, i’d guess it might heat up by 3 degrees Celsius in a day. Heat is shed only by radiation in a vacuum, so only a portion of that heat would leave that space over the night. I couldn’t tell you how much, that is too sophisticated a calculation for me to even estimate. But it is safe to say that after maybe 3 months, if the extra heat wasn’t passed into the Gallery or shed by a small radiator over the course of the night, that space would feel too warm. Not sweltering, just too warm.
In the case of the dome, for the sake of making life easy, it would be good to put a layer of that smart glass on the outside, that changes opacity when a charge is run through it. The sun is pretty bright during the day so that would make it much more pleasant to be inside, aside from making it simple to fine-tune the interior temperature.
In short, there will be no problem regulating the temperature of the habs.
(Note: Health Tips on the Moon - Part 2 shows the Sports Hab, and the Sketchfab on the main page labelled Gallery Lunar Habitat shows the Gallery and the dome at the bottom of it - it is the 4th one, you have to scroll down a bit.)