>>10834436where the energy is stored. kinetic energy in the form of moving/rotating/oscillating atoms/molecules (well, caveat -- a lot of the time these "modes" of kinetic energy have to do with molecular potential energy, so for example if it's a diatomic molecule where the atoms are moving in a springy fashion where the molecule is stretching then contracting then stretching or the same thing just in terms of bending and unbending and then bending the other way, then there is some transfer of kinetic energy into potential energy and back in some sustained way, but let's just consider this to be kinetic for now).
photon emission heat is more when you have something where these kinetic modes don't exist but electric shell energies do. it's hard to even think of an example of this, but maybe one could think of something like a solid-state laser where only the surface of some semiconductor is actually "hot" because the atoms are very tightly held in place but the electrons on the atoms of that layer can be excited. that's rare though, for table top experiments.
in particle physics one can interpret the center-of-mass energy of a collision as a sort of temperature; in that case you could think of kinetic energies of the particles (as physicists usually do) but alternatively, say if you have a high-energy collision like at LEP where they collided electrons with positrons, the two particles just annihilate and put their energy into the QFT vacuum. and in the thermodynamic way of looking at that, the vacuum itself is excited into an EXTREMELY hot state. like 10^10 kelvin (i am pulling that number out of my ass but it's huge like that). and you could think of that region of vacuum going into some sort of "photon emission" state where it wants to radiate not only photons but all sorts of particles. so in that case you also get something that looks like the energy is mostly in terms of radiation (since the vacuum has nothing in it to store the energy in kinetic modes)