I have no doubt thermal conduction is a useful model for heat transfer, wherein kinetic energy is transferred between particles when they collide. However, according to explanations that I believe are canonical, two molecules collide due to electromagnetic repulsion (and possibly Pauli Exclusion) of their electron "clouds". In the standard model of particle physics, electromagnetic repulsions between electrons occur via the exchange of force-carrying particles, which happen to be photons. (Virtual photons, if I'm not mistaken, and perhaps that is an important point here.)

So, if thermal conduction is microscopic kinetic energy transfer due to molecular collisions, and molecular collisions occur by the exchange of photons, then it appears to me that at a fundamental level thermal conduction is a special case of energy transfer by photons, which in my understanding, is the radiation mechanism of heat transfer.

Is this conclusion incorrect (and if so, why)?