Superconductors are actually very poor thermal conductors, the reason being that the charge carriers (Cooper pairs) do not carry entropy/heat, otherwise they wouldn't be superconducting to begin with. Good thermal conductors allow dissipation to travel quickly and effectively. In principle, density fluctuations of Cooper pairs could carry heat quite effectively, but in charged systems this has a very large energy cost due to Coulomb repulsion (i.e. excitations are gapped) and so cannot happen under normal circumstances.
On the other hand, neutral superfluids such as superfluid liquid helium are excellent thermal conductors. Unlike charged systems, density fluctuations (second sound, phonons/rotons) do not have an energy cost (i.e. they are gapless) and can carry heat extremely well. In fact, superfluid liquid helium is by far the best known thermal conductor of all materials. You can read more about it at the link below