Internal reflections, of whatever efficiency, simply even out the internal temperature variations. I have a reference somewhere, though sketchy, gave some reflectance vs. temperature. I don't have it on my website. So I will try to find it to night. There are things that are highly reflective that aren't conductors.
Electrical conduction is a easy parameter to use when using metals.
The deal with metals is that the electrons are mobile. However, and I am shaky on the theory, is that electrons that are not tightly bound to the nucleus are the ones that exhibit high reflectivity. Even though the electron is trapped in the atom it has considerable movement. This movement can transfer charge to its neighbors. It's the movement of charge the forms the conductive inverse image of the electromagnetic wave as it hits the surface.