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That one is probably out of my pay grade.

One guess is that the Moon is not a perfect reflector and the photon density per unit area coming off the Moon is a lot lower.

You could test this hypothesis by pointing a laser thermometer at a light bulb and a pile of dirt reflecting the light from the bulb. The Moon is basically made out of gray dirt.

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Ground in the shade may have some insulation? You'd think open ground would be warmer at night because it's unshaded, and because the moon is supposed to be reflecting sunlight. The fact that it's colder is counterintuitive.

It would be interesting to try the experiment on a moonless night to check the difference between open and shaded ground. If they are the same the shade doesn't likely matter (given a sufficient time from sundown).

You could do the light bulb dirt test in a room without windows or another light source.

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