"The IR the Earth receives from the hellishly hot surface of the moon is the real cause of global warming. Well done gb, another scientific orthodoxy upended."

Well, it's couldn't cause global warming because it a fairly constant factor- over decade of time the energy would the same, as over centuries of time- it might vary on a monthly time scale. It probably can't have large impact because I'm sure that someone would noticed such a large difference. The any heating would be on the upper atmosphere, but should also affect the lower atmosphere temperatures, and so be measurable at ground stations.
I would guess that up to a 1 C monthly difference may not have been noticed, but 2 C or higher probably would have been. I guess looking at monthly satellite data might be a way to "measure" any effect, even a .5 C difference should show up.

But as I said I don't know how much infrared from the Moon is reaching the Earth's upper atmosphere. I'm pretty sure it is more energy than the visible light- around 10 times as much.

Keep in mind that I would consider a watt per sq meter as significant, I'm not imagining tens or hundreds of watts per sq meter.
Obviously the Sun energy easily overwhelms any reflected energy from the Moon.
In terms of visible light as seen by the human eye:
Sun:
32000 lux Sunlight on an average day (min.)
100000 lux Sunlight on an average day (max.)
Moon:
0.25 lux Full Moon on a clear night
1 lux Moonlight at high altitude at tropical latitudes
http://en.wikipedia.org/wiki/Lux

About 1/2 of the Sun's energy is in visible light and with the Moon about 1/10th of it's energy is visible light. And obviously the Sun's infrared [which a large portion of it's energy] is a different wavelength band than the Moon's infrared.