Moon's negative greenhouse effect? - Astronomy

You don't say how you got your average temperature. If it is a straightforward average, then I think I have your answer.

The temperature of the moon is highly non uniform, ranging from around 100 K on the night side to 370 K on the sunlit side. This gives a crude average of 235 K.

http://space.stackexchange.com/questions/3290/what-is-the-temperature-variation-between-the-lunar-day-and-night-on-the-moon

However, in terms of blackbody radiation, if we treat both hemispheres as separate blackbodies, then together they radiate as much energy as a hotter blackbody because of the $T^4$ factor in Stefan's law. The "effective temperature" will be
$$ T simeq (0.5times 100^4 + 0.5times 370^4)^{0.25}= 311 K$$
So this is more like your equilibrium temperature and a more appropriate area weighting and/or tweaks to the exact range of temperatures could bring it into close agreement.