SAMU,
I going to try once more to come at this from a different direction.
Imagine for a moment that when the CSM/LM stack was launched into translunar orbit, something else was sent along: a very large, perfectly reflective mirror, one designed to allow no radiation to penetrate, and (for good measure) to stay cool so that it didn't radiate significantly in the IR from the backside. This mirror is arranged such that the CSM/LM is in its shadow completely, all the way to the moon.
Now, we remove the astronauts and turn off all the electrical equipment (including the cooling systems). Thus there are no internal heat sources, and the spacecraft is totally shielded from the sun -- as effectively, say, as if it were on the unlit side of the moon.
You would agree, would you not, that in such circumstances, the capsule would get very cold? Even though there is no active cooling going on?
All right. Now put in the astronauts, but leave the equipment turned off. It would be a bit warmer (as long as the astronauts remained alive), right? But not hot, by any means.
But, you say, there was no mirror, no "parasol" for the Apollo spacecraft. But there was! The designers knew that they had some 1500 - 2000 watts of heat to dissipate from the electrical systems alone, and would have to provide lots of cooling capacity for it. They didn't want to make those systems any larger and heavier than necessary.
Therefore, they designed the spacecraft to absorb as little solar energy as possible. Of course, their "mirror" wasn't perfect, so the heat dissipation systems were made big enough to deal with that. But they did a pretty good job, so good that when the electronics and most of the refrigeration was shut down, the solar gain wasn't enough to keep the interior very much above freezing.
For your scenario to be correct, the Apollo designers would have to be incompetent fools, who couldn't figure out how to keep the sun at bay and therefore added vast amounts of unnecessary weight to provide the cooling capacity to re-radiate what they couldn't reflect away in the first place.
So, were the Apollo designers incompetent fools, or were they not?
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