IDK the truth of it all, but how did they survive the cooking hot temps of direct exposure to the sun? Or the freezing cold temps of space? Keep in mind that to transfer energy takes energy. Running AC or heating electrically? Not possible for any length of time, with the battery power in 1969. No solar sails were on the capsule. Where did the juice come from?
If you are going to tell me they kept the ship rotating, that is a joke.
The Landing Module had batteries for 40+ hours of use (descent to and activity on the lunar surface and ascent to rendezvous) and the Command Module had batteries for re-entry operations (about 15 minutes of use). For the rest of the mission, electrical power came from the fuel cell in the Service Module.
Remember there's no air to conduct heat in space. In that respect, it's like the vacuum between the inside and outside bottles of a Thermos. So the only heat transfer that can take place (unless you jettison mass, see below) is radiant transfer. That means that, as long as you are careful about the amount if infrared you absorb from the sun, your heat loss due to radiation is going to be fairly small, and you can control your temperature pretty effectively.
The flight avionics and other equipment on board Apollo generated a fair amount of heat. (And, since the only heat loss is radiative, it stayed mostly on the spacecraft.) When Apollo 13 had to turn all that stuff off, the spacecraft gradually got very cold, despite being in direct sunlight for almost the whole trip. Parts of it got below freezing.
Keep in mind that to transfer energy takes energy.
Only if "uphill" against entropy.
Climate control of spacesuits during moonwalks is a whole other topic. The problem -- remember this was in lunar daylight almost exclusively -- was keeping the astronauts cool. You can't run a conventional A/C system because it has no place to sink the waste heat because it's in a vacuum. So the "air conditioner" relied on cooling by evaporating water. Once the onboard water supply ran out, that was the end of the moonwalk.
No solar sails were on the capsule. Where did the juice come from?
Do you mean solar cells? The Apollo command and service module ran off fuel cells powered by hydrogen and oxygen. The byproduct of the fuel cells was water, which where the astronauts got their water for drinking and washing. The lunar module had onboard batteries, which were ordinarily good for about 3 days or so.
They had to build a modified Apollo service module for Skylab, which involved docking to a space station for up to 84 days. Fuel cells were only useful for about two weeks and couldn't be shut down & restarted in space, so they removed some of the fuel cell hardware and replaced it with batteries to get the astronauts back to earth. (The batteries could be charged by the solar panels on the station.)
And just what did they use for computing power?
https://www.history.com/news/moon-landing-technology-inventions-computers-heat-shield-rovers