[michwill]

Well, this doesn't look right to me. Imagine that the moon is actually a filter at the path of the sunlight.

Sun's temperature is 6000 K. Moon's surface is pretty black: it reflects only 12% of the light.

So, effective temperature of the Sun reflected by Moon, considering that thermal radiation is proportional to T^4, is 6000 * .12 ^ (1/4) ~= 3500 K. That's quite enough to light up some fire! Of course, the spectral composition of the light will be not thermal etc, but the estimate should be close enough.

Why doesn't the Moon itself heat up like that? Well, the rocks on Earth don't heat up to 6000 K either... I think, it's partly that they are "not surrounded by sun", partly that the Moon is a giant cold heatsink