At a guess, the moon is a diffuse rather than a reflective surface, so it's going to be closer to a maximum of the lunar surface temperature than to solar surface temperature.
An atmospheric lens, however, will reach a maximum of somewhat closer to solar surface temperature, though still lower because of scattering and absorption which definitely isn't trivial on this kind of scale.
If it had an albedo of 0% it would be a black body and be radiating only thermal radiation at its surface temperature; it's not too far away from that but it is reflecting some "black body" radiation from the sun representative of a higher temperature.
An atmospheric lens, however, will reach a maximum of somewhat closer to solar surface temperature, though still lower because of scattering and absorption which definitely isn't trivial on this kind of scale.