I have read this question:
This is because of Kirchhoff's law of thermal radiation. The corollary from it is that emissivity of a material is equal to its absorptivity.
a body must absorb and emit identically at a given wavelength. Transparent is a terrible emitter.
These answers specifically explain that though every objects glows in a sense when heated (just some not in the visible range), in the case of diamond, heating it will not cause it to simply emit visible wavelength photons.
Thus diamond will not emit visible light, since it is remaining transparent when heated, and can only emit little number of visible wavelength photons.
Though, this explanation does not work for glass. If you heat glass, it emits visible (glows), meaning either of two things:
it absorbs visible and re-emits visible
it absorbs all wavelength and re-emits visible (in cascades or for other reasons changes the re-emitted photons' wavelength relative to the absorbed ones)
- Why does hot (molten) glass glow, while diamond does not?