First of all I want to apologize if this is a stupid question. I'm a layman who's merely very interested in physics, without a degree to my name.
I was trying to research electric superconductors lately (in parts due to the news regarding LK-99, to nobody's surprise) which prompted a question in my head regarding the feasibility of thermal superconductors.
From my very limited understanding, thermal energy transfers occur either through the emission and absorption of photons given off an excited electron as it moves to a lower energy state, or electric field interactions of phonons. However, what I was wondering about was:
Since thermal energy transfer always moves in the direction from higher to lower energy states, what is the physical limitation that causes thermal superconductors not to be feasible (assuming they are not)?