The total intensity is determined by the mass of the black body (larger objects give off more energy).
[b]The intensity of the radiation produced by a black body is dependent ONLY on the temperature.
It is NOT dependent on the mass.
Kind of obviously more power is emitted by a body with a larger surface area, everything else being the same. So something could cool faster if it had a larger surface area - I agree it's nothing to do with mass. Temperature determines both the intensity and the energies of the individual photons, but not total amount of radiation (there's a special word for that which I forget).
On a clear day about one quarter of the visible spectrum is absorbed by the atmosphere.
So the other 75% heats up the ground :P
The fact that we see in the visible spectrum is kind of interesting. It's not just by chance. The visible spectrum happens to be located right at a spot where water has a massive increase in transmissivity. So under the sea or, I suppose in wet air, or in an animal with eyes filled with water (like ours) things would be pretty dark at any other nearby wavelength.
