On the atomic level, how is incandescent light structured?

Question

I want to know from the smallest possible originating structures how the light I see generated from heat is made by atoms themselves.

Answer 1

As Olin says in his comment, the light you're asking about is the black body radiation.

Black body radiation is a collective phenomenon, that is it's not generated by individual atoms. Heating a solid causes the crystal lattice to vibrate, and the vibrations scatter electrons in the solid and cause transient oscillating dipoles. It's these oscillating dipoles that radiate EM just as any oscillating dipole does.

It's worth noting that the black body spectrum is actually determined by statistics, and the exact mechanism of it's generation doesn't matter. See What are the various physical mechanisms for energy transfer to the photon during blackbody emission? for a discussion of this.