The outer layer temperature is fixed by convection from within, not radiative transfer from outside. Therefore, although the corona temperature is several orders of magnitude higher, for reasons that aren%26#039;t clear but likely aren%26#039;t due at all to radiative transfer, the point is that the number of watts per meter squared coming from below the surface are huge compared to the watts per meter squared being delivered to the surface from the corona. The analogy to Earth would be if the Earth%26#039;s core were several million Kelvins instead of several thousand. In that case the solar flux and greenhouse effect would be irrelevant in determining the surface temperature (aside from the fact there would be no atmosphere to speak of).
I think.
What did you get?
