Very very simplistically.
Heat is kinetic energy. The transfer of kinetic energy as heat is through conduction, convection, or radiation.
The energy, as heat, can be considered as kinetic as a hot particles (atom, electron, or ion) has an associated velocity (on a quantum level) as this particle interacts with other particles (collisions) some of that kinetic energy is transferred (conduction).
If these particles are easily able to move (fluids) that kinetic energy moves with the fluid (conduction).
If the energy difference between particles is sufficient the energy transmission can be electromagnetic (radiation). Kinetic energy transmission by this method can be over large distances without intermediate media (matter).