I don't claim to understand it, but we are not in the position to judge what moonlight should or should not do based on rationalism when we have numerous empirical experiments which tell us that moonlight cools.
Have a look at CuriousSquirrel's post and the YouTube video. Empirical evidence that sunlight makes things cooler?
The explanation is given in the video. Honestly. Cold light. If you could prove that in a way which doesn't make scientists laugh out loud you would win a Nobel prize.
I looked at the video and its just bad. First he points a telescope at the moon and then he moves the telescope to compare the temperature to empty space. He may as well compare the temperature of the moon to the temperature of an ice cube... That experiment does NOT tell us whether the light of the moon can make things cooler.
Next he makes some ridiculous claim that when you sit in the shade it is actually warmer. The example he gives involves putting a piece of foil in the sun and then putting it under a bush. Under the bush it is warmer. This is ridiculous. In the day time it is not warmer in the shade than it is directly in the sun.
He says the foil is like a mirror reflecting ambient IR of the objects around it. The foil is of course physically cooler in the shade, but the reflected IR is not. However, this does not explain experiments with non-laser thermometer devices taking a direct measurement of bodies which shows the same cooling moonlight effect.
None of the above really even tests the issue, and is an attempt to discount the tests based on flawed rationalism. Cooling moon light is not directly tested by that experimenter. Sweeping declarations and assumptions are made.
If moon light did not cool, then it should be easy to design an experiment that shows that.
The experimenter in that video and the excuse masters on the internet do everything except that.Rowbotham references an experiment performed by a notable mid 1800's scientist in which a telescope was indoors and closed to the elements, looking out a window at the moon. A room temperature thermometer was placed next to the eye piece and the temperature cooled. When removed it warmed again. This happened again and again.The excuses given do not describe what is happening there.