As I understand it, photons (and other gauge bosons) have effective mass but not “rest mass”. Think of a wave on the ocean: the wave itself has no rest mass, because when it is not moving, it does not exist. The wave is created by an external force and translates that force across the water. When it capsizes your dory or carries a surfer toward the beach, you can see that it has effective mass, but after its energy is expended, it is no more (this also kind of illustrates the interrelation between energy and mass).
A photon behaves like a wave in this respect. It is produced by an electron as the electron loses some energy, then propagates along its path like a wave until it imparts its energy to another electron (is absorbed). Since heat is an aggregate measure of energy, photons themselves can be seen as a heat carrier. After all, almost all of the heat we receive from the sun is delivered via radiated photons. And since energy increases with frequency, the “color” of a photon could reasonably be used as a measure of its “temperature”.