In this question the relationship between characteristic spectral lines of elements and the apparently continuous emission of blackbody radiation was examined.
It was suggested in the answer that there is essentially no difference between the two and that BB radiation is simply the result of really large molecules' orbitals overlapping, creating so many different energy levels that the light emitted seems a continuum. This seems somewhat believable and somewhat dubious, especially as this idea is regularly contradicted by answers elsewhere on the site (such as in this question, where the second answer says, "This phenomenon arise as an entirely different cause." when contrasting emission spectra with BB).
Why would this work with the Sun? The argument suggests that one percieves continuous spectra like BB radiation in cases where the object heated contains large lattices or molecules bonded together, but neither exist in the Sun. The Sun will mainly contain Hydrogen and Helium - both of these have quite "sparse" spectral lines. Even if their spectra were "stretched" right and left by doppler shifting, you wouldn't expect this shifting to stretch to almost all of the visible spectrum... Yet, when we look at the Sun, we see an almost continuous spectrum of light (with small absorption lines caused by the "atmosphere" of gas around it).
So the answer cannot be correct, or only captures part of the truth. What is the answer?
Interesting note: A friend wondered whether it would be the result of atoms' and molecules' nuclei being greatly charged bodies moving around in a heated body at such great speeds that they naturally emit a photon (as an accelerating charge would be expected to), however we found that techniques which look at this (which does happen) such as Raman Spectroscopy are called "long-wave spectra" because of how the light emitted is typically at non-visible wavelengths.
