So are trees and yet they reflect plenty of IR from the sun, as do most rocks, of which the moon is constructed last I checked. Camera IR is shortwave (well under 1um) which means that the temperature of the body is irrelevant (unless very high) and you're relying on illumination from a hot source (sun).
Originally Posted by Sirius Glass
If you want to see heat around the 20-200C range, you need a multiple-micron sensor and it needs to be refrigerated otherwise its own temperature (and longwave IR emissions from within the camera) will completely obliterate the image.
As to metering, the moon is "sunny-11" on a clear night, i.e. f/11 t=1/ISO, e.g. f/11 ISO100. So with IR820+R72 where 1s f/16 works in full sun, I would expect that 1s f/11 or variations thereon (1/8 f/4?) is probably about right to get a decent moon exposure depending on the rock composition. Exposures any longer than half a second will show very distinct motion blur unless you have a tracking mount.