From my direct IR measurement experiences, materials with nitrides (N, N2, etc) and oxides (O, O2, etc) in their surface composition have
very high emissivity, closer to blackbodies.
Ceramic has
a very high emissivity rating, meaning it produces a lot of infrared heat.
Not exact matches
The
emissivity of earth (and the oceans) is
very high.
Then try 1365/4 for the flux and
emissivity of 0.88 (which is closer to that of rock and soil) and you get 287.6 K which is
very close to the assumed mean surface temperature and thus obviates any need for that «33 degree of warming» In fact the 0.88 should be even lower and that gives
higher temperatures above 290K.