Ill try and shed some light on the topic.
"Heat" is a measure of the kinetic energy of the particles that make up the metal bar ( at least the heat you feel from the bar ). That heat is conducted by the metal as the molecular excitations that travel along the bar ( vibrational mostly ).
Some energy will be transferred as EM radiation, because you can see the flames. You won't feel this as heat until it hits your skin and excites your skin, giving it (skin) more kinetic energy.
EM radiation is caused, or emitted, by the relaxation of atomic orbitals from excited energetic states. During the combustion of the fuel, chemical energy is released making the molecules move and vibrate faster (chemical energy used here abstracts away the details of molecular quantum mechanics, which is mind boggling), but also their electronic configuration is excited, sometimes for fleetingly short periods.
When the excited states of electrons decay back to their usual energies, they must do so according to quantum mechanical rules (i don't know who told them this, but they listen anyway) which restricts them to quantised lumps and jumps.
The difference i guess is that EM radiation is the kinetic energy of a photon, and the heat conduction is the kinetic energy of a molecule of the bar.
When does each form happen?
Im not sure, its a good question. I can't answer that very clearly.
(And in so answering this post i unmask the veil of my capacitance & resitance ignorance).
