Where do Photons in Hot "Box" Come From?

This is a little bit of a chicken-and-egg problem, because the way that we humans on Earth change the temperature of anything we might call an "oven" is to start with electromagnetism.

For instance, when I heat the oven in my kitchen, I close a switch that connects the two ends of the heating element to an oscillating electric potential difference. This sets up a time-varying electric field in the element, so that electrons in its conduction band are accelerated relative the stationary ions that make up its crystal lattice. Inelastic collisions between the mobile conduction electrons and the ions cause the ions to move, but because the solid's crystal structure is stable, that ionic motion gets converted into lower-energy collective oscillations of the entire lattice. The vibrating ions at the surface of the heating element tend to increase the kinetic energies of the cooler gas molecules when they collide, so the gas in the oven heats up.

The thing to notice here is that every step in this process is an electromagnetic interaction. The energy from the power company makes the heating element hot because of the local shape of the electromagnetic field. The atom-atom interactions that transfer energy within the heating element, and from the heating element to the gas that touches$^1$ it, are purely electromagnetic interactions. The dull red photons that the hot wire emits are happening because the lattice ions in the wire, which start off oscillating wildly after striking a conduction electron then later oscillate less wildly, are charged particles undergoing electromagnetic transitions. The photon is the particle which mediates electromagnetic transitions. Photons are involved at every stage in the process.

If your oven is gas instead of electric, it's still an entirely electromagnetic process: the gas combustion reaction

$$require{mhchem}ce{CH4 +2 O2 to CO2 + 2 H2O}$$

is an electronic exchange that happens during sufficiently-energetic collisions. Chemistry is just ("just") applied electromagnetism.$^2$ The photons that make a candle flame or a campfire radiantly warm, and that fill up a carbon-burning-fueled oven, come electronic transitions in this reaction.$^3$

The reason that only electromagnetism figures into these discussions is that electromagnetism is the only fundamental interaction mediated by a massless field, so electromagnetism is still active as a heat-transfer mechanism at the low temperatures where neutral matter is stable and we are alive. An "oven" that maintained its hot interior without material walls could eventually get hot enough to excite other quantum-mechanical fields. The first of these is electron-positron pair creation, though a QED purist might say that's just a feature of the electromagnetic field. The first new interaction to contribute happens when the highest-energy particle collisions start to produce pions. Pion decay couples your oven's temperature to the neutrino sector, which is a big change in its thermodynamics.

As we understand the Big Bang, the temperature cooled from an initial condition of infinitely hot temperature and infinitely dense matter, which permitted all of the various quantum fields to reach thermal equilibrium with each other.$^4$ In particular the neutrino sector is believed to have reached thermal equilibrium, so there is a universe-filling background of primordial neutrinos with an energy spectrum like the universe-filling background of primordial photons, except slightly colder, because the neutrinos decoupled earlier in during the initial expansion of the Universe.

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$^1$ The convection process that distributes the heated gas around the oven has more to do with statistics, but the individual particle interactions are electromagnetic.

$^2$ See footnote 1.

$^3$ It's my understanding that the blue light from a burning-hydrocarbon flame is emitted by molecular transitions from $ce{CO2}$ and $ce{H2O}$ as those molecules relax down to their ground states, and that the yellow light is blackbody radiation from hot soot particles. But I don't remember whether I read that from somewhere reputable or whether I figured it out myself.

$^4$ Dear fellow pedants: fixing the oversimplifications in that sentence could fill a thick and very interesting book.