In other words, what happens if a particle of matter is heated up enough to radiate light, but the particle much smaller than the wavelength of the light it is trying to emit. Does it still emit? If so, how? Does it "bottle up" heat inside itself until its temperature gets high enough to emit at a wavelength compatible with its size? For some nanoparticles, such a temperature would vaporize them or even ionize them.
Can a point source be a tiny fraction of one wavelength in its longest dimension?
I certainly can’t answer your question. Way over my head.
“In other words, what happens if a particle of matter is heated up enough to radiate light, but the particle much smaller than the wavelength of the light it is trying to emit. Does it still emit? If so, how?”
Yes, it still emits. I think what is tripping you up is thinking that it needs to emit the whole wavelength. It doesn’t. It just needs to emit a single photon, which is practically 2 dimensional. The photon is what oscillates over the wavelength, after it is emitted.