Heat or thermal energy as understood is nothing but motion of molecules of the matter. If the molecules are tightly bound (in case of solids), it is to-and-fro molecular vibrations, otherwise it is continuous random motion of molecules (in case of liquids/gases/plasma).
Sound, being waves, is also vibrations in matter. Why, then, if we heat one end of a solid rod, assuming rod is at least few feet in length, does it take ages for the heat to reach the other end, whereas sound reaches in no time ? (sound travels at 1400 m/s in solid)
Doesn't it show that heat is more an intra-atomic feature rather than an atomic or molecular motion? Observation that electrical good conductors are also good conductors for heat, can we assume that heat is chaotic motion of electrons (the "electron gas")? (Of course, all the known phenomena related to heat will be needed to be explained with this hypothesis.)