I dunno - like I say it's difficult to get definitive data on this for some reason.
BUT - remember the sun isn't simply an object that has been heated up to a given temperature and is now radiating. It's pouring out radiation through an atmosphere, so there's absorption at the surface. And, it's not black. Carbon nanotubes are the best approx to blackbodies (that we have) and that's about 99% emissivity. A blackhole is black, but it's fairly cold....
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