"The output energy of a hot object scales as T^4. Sun surface temp ~6000K Moon surface temp, let's say 100K."

The Moon is temperature is:
Mean surface temperature (night) -153°C
Mean surface temperature (day) 107°C
http://www.solarviews.com/eng/moon.htm
In K: 120 K [night] and 380 K [day]

And I'm mostly talking about when you have full moon with the side facing Earth is 380 K.

There additional complications because with the Moon one is dealing a more curved surface compared to the Sun [and comparatively a far rougher surface {considering scale and distance}]. If the Moon was a flat disc it would be hotter, if it was a smoother surface it would be hotter. The Moon's curved shape and roughness increase it's efficiency as a radiator, thereby lowering it's temperature- it puts out more energy than a flat smooth surface would of same diameter.

Moon: Equatorial radius (km) 1,737.4
Sphere (surface): 4 x pi x radius2
Circle pi x radius2

Moon total area: 37,932,296 sq km
Hemisphere: 18,966,148 sq km

Circle: 1,737.4 radius : 9,483,074 sq km