This paper discusses relativistic corrections to the thermal Coulomb potential for simple atomic systems. The theoretical description of the revealed thermal corrections is carried out within the framework of relativistic quantum electrodynamics. As a result, thermal corrections to the fine and hyperfine structures of atomic levels are introduced. The theory presented in this paper is based on the assumption that the atom is placed in a thermal environment created by the blackbody radiation. The numerical results allow us to expect their significance for modern experiments and testing the fundamental interactions.