Based on fully finite temperature field theory we investigate the radiation probability in the bremsstrahlung process in thermal QED. It turns out that the infrared divergences resulting from the emission and absorption of the real photons are cancelled by the virtual photon exchange processes at finite temperature. The full quantum calculation results for soft photon radiation coincide completely with those obtained in the semiclassical approximation. In the framework of thermofield dynamics it is shown that the bremsstrahlung radiation in thermal QED is a coherent state and its quasi-classical behaviour leads to the above coincidence.