The equilibrium temperature of a polished aluminum surface at 1AU from the sun is 416K, hot enough to melt polyethylene and at least weaken many of the relevant aerospace plastics like the PET in mylar film.
Painting polished aluminum black drastically raises emissivity along with the lowered reflectivity, and brings its behavior closer to a blackbody.
So does allowing aluminum to oxidize, which it does almost instantaneously in atmosphere. So it's not like it's going to change anything drastically.
The reason this seems like it should change things a lot is that you're used to convectively cooled matte surfaces on Earth, where emissivity and radiative cooling is a less relevant factor and the only significant effect of painting something black is primarily that it absorbs more energy.