The process of recombination for the hydrogen atom in the heat bath creating the blackbody radiation is described within the frameworks of quantum electrodynamics. For this purpose the self-energy for unbound electron in the field of the nucleus is considered. The imaginary part of this self-energy is directly connected with the recombination cross section. The same procedure is applied to the hydrogen atom in the field of blackbody radiation. This leads to a thermal correction to the process of recombination for the hydrogen atom in the heat bath.