Why is moon light cold? Why is light from the moon cold? For example full moon light shining on a surface or material will cause it to be colder than a surface or object nearby that is shaded from the moonlight. What causes this phenomenon?

 A: Probably the heat radiation from the object that you blocked the moonlight with is the cause. Also if the blocking object was close then you not only blocked the moonlight but also part of the sky, which has a very low radiation temperature. You can cool the object or use an object with very low emissivity in the infrared. I am assuming that all other radiation/heat sources, such as humans, had exactly constant impact in the experiment.
A: As my2cts said, it may be attributable to the way you blocked the moonlight. In image this is:

If excessive blocking area is used then you are not only blocking radiation from the moon but also radiation coming out from the water into the dark sky, thus preventing water to cool.
Try, if possible, to repeat the experiment making sure to use a "proper blocking area" and tell us the results. Or tell us if you have already used a "proper blocking area" to look for other explanation. 
A: In thermal infrared, the moon is partly obscured by the atmosphere. The atmosphere has a bit of a window from about 8 micrometer to about 13 micrometer, the region of thermal infrared that your Fluke is probably sensitive to. 
However, there is absorption by ozone centered at $9.6\ \mu$m, which will affect the image to obscure the Moon. The emission at these wavelengths will brighten the background.
