What is the most thermally conductive material in the universe? (natural or synthetic)?

Question

I know that copper and silver are neck and neck, with diamond dominating copper five-fold. I've heard that liquid He is like a thermal super conductor in its super fluid state, but I have yet to see the numbers.

Answer 1

The most thermally conductive material in the universe hasn't been discovered yet.

Answer 2

Diamond is the best thermal conductor at room temperature. High purity oxygen free copper's conductivity climbs by orders of magnitude as the temperature falls toward absolute zero. I don't know what is best near zero kelvin, though.