Process of transferring kinetic energy in regard to photons.
You may be experiencing a very common misconception, which I blame on Star Trek and Star Wars and all their talk of pure energy that always comes as bright lights, with the implicit assumption that energy is some kind of fiery bright substance, like a glowing fluid or something.  It isn't.  Energy is a property of matter, and of the rather peculiar substance we call electromagnetic radiation, chunks of which are called photons.  Think of energy as kind of like an adjective that describes a noun (some kind of matter, or radiation).  An atom can be energetic or not energetic, and so can a photon, just as a cat can be furry or not furry.  But you would  never mistake "furriness" as some kind of object itself.  In the same sense, you should not mistake energy as some kind of substance itself.  It's a property of substances, just like furriness is a property of cats.

So energy has to be transferred from a hot substance to a cold one, and indeed it could go by way of photons.  One particle could emit a photon, transferring part of its energy to the photon, and maybe slow done, and then this photon could be absorbed by another particle, which would receive the transferred energy, and maybe accelerate (go faster).  That's definitely one way it could happen.  But it doesn't have to happen that way, because energy can be transferred other ways.  For example, the first particle could simply run into the second, bang, and the impact itself could transfer the energy directly, no photons involved.  Or the first particle could run into a third particle, or the wall of a container, and the second particle could pick up the energy from the third particle, or the wall of a container.  And so on.