There's a very simple explanation for the whole "thermometer in the shade vs thermometer in the moonlight" thing. Just go do a quick internet search.

Here's a simple experiment: if moonlight is what is cooling the thermometer, why do you observe the exact same effect on a clear night with no moon? Go try it; you'll see the same "cooling" effect in the open air vs beneath a tree or some other "shade" even when there is no moon.

If the moonlight were the cause of the cooling, then you would not see the same effect when there is no moonlight. But you do see the same effect when there is no moonlight. Ergo, the cooling in the shade must be caused by something other than the moonlight.

It's caused by the fact that the earth warms up during the day (because the sun is shining on it), and during the night it cools off. "Cooling off" consists of emitting heat (i.e. the heat leaves the ground and escapes upward into the air). If you are in the "shade" i.e. under a tree or a roof of some kind, that escaping heat is trapped by the cover, and the air stays slightly warmer than it does when there is nothing above you to trap the heat.

You are ass-uming that The Moon's light source is reflected light from The Sun.  If however, The Moon were capable of absorbing Sunlight and then glowing at nightime, it would be capable of producing a Full Moon, observable from different angles of view at the same time.  


"Luminescence is emission of light by a substance not resulting from heat; it is thus a form of cold-body radiation."

"This distinguishes luminescence from incandescence, which is light emitted by a substance as a result of heating."

"The dials, hands, scales, and signs of aviation and navigational instruments and markings are often coated with luminescent materials in a process known as "luminising.""

https://en.wikipedia.org/wiki/Luminescence