[Slides]

Anodizing adds a layer of aluminium oxide (which carries the tint), which is more thermally insulative, although not that bad.

Even if you don't believe established emissivity theory and have no formal physics learning, an anecdote from someone who used controlled conditions may give you a clue.

I have a mate who before painting bits in his engine bay experimented with a rubbed back (to remove the red surface finish) bare aluminium coke can and one painted black, filled with water from the same kettle, black one cooled faster, as black body radiation theory would suggest, despite the fact it was covered in paint.

I would suggest leaving it bare or a light coat of black. There is a reason copper radiators and OEM steel sumps were always sealed with black paint.