
Indeed, the sky doesn't look much like a black body if you look carefully
enough; in particular, its temperature at radio frequencies is quite a
bit higher than you would see from a black body.  Morgan&Gordon's fat
"Communications Satellite Handbook" has a graph of sky temperature vs.
wavelength, in fact, for communications design.

However, in terms of energy content, the RF frequencies are negligible.
For thermal purposes, at very large distances from the Sun the sky
looks like a black body at 3.5K (Allen, "Astrophysical Quantities").
I haven't found a number for non-large distances, since solar radiation
tends to be something you can't just ignore :-), but M&G says "about 4K"
in a brief discussion of why solar radiation dominates the problem.