Remember that when a crystal is cooled to absolute zero, the atoms don't stop moving, they still jiggle. Why? If they stopped moving, we would know where they were and that they had zero motion, and that is against the uncertainty principle. We can't know where they are and how fast they are moving, so they must be continually wiggling in there!$_1$
The atoms and molecules are composed of charged particles, i.e., protons and electrons, and kinetic interactions among matter particles result in charge-acceleration and dipole-oscillation. This results in the electrodynamic generation of coupled electric and magnetic fields, resulting in the emission of photons, radiating energy away from the body through its surface boundary.$_2$
So, every object at "any" temperature has certain probability of emitting photons.
Credits: $_1$*The Feynman Lectures on Physics-Vol.1Page-2-10* Page no's are subjected to change depending on editions.$_2$Wikipedia-Thermal raiation