OK, let's break this down then.

We have seen from Grant's equation on page 2 that an object in space covered in highly reflective material as the Apollo spacecraft was will not heat up above freezing due to incoming solar radiation. Sunlight is therefore not enough to create an overheating problem in the spacecraft.

Does the cooling system work as advertised? Well, for the Apollo 13 question that this thread began on this is not an issue because the cooling system, along with everything else, was shut off during the coast home. For everything else it is an issue, because if the cooling system could not operate as it is said to have done then the whole of Apollo becomes suspect.

On Apollo 13, then, it seems the only source of heat inside the cabin was the astronauts themselves and whatever sunlight may have come in through the windows to warm the interior.

So, the key questions seem to be:

What equilibrium temperature will an unpowered Apollo spacecraft on a translunar or transearth coast reach?

How long will it take an unpowered Apollo spacecraft with three men inside to reach this temperature, or what temperature could the cabin interior reach during the time the spacecraft was powered down?

Can the Apollo cooling system work effectively to maintain a comfortable environment inside?

Assuming that you have performed your own calculations to arrive at your previously stated conclusions, IDW, what do you have as answers for the first two questions, and why do you believe that the answer to the third is 'no'.?

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"The very powerful and the very stupid have one thing in common: They don't alter their views to fit the facts, they alter the facts to fit their views." The Doctor, Doctor Who: The Face of Evil.