In this paper a type of thermal corrections for the helium and heliumlike atomic systems are introduced. These are the thermal one-photon exchange between the bound electrons and nucleus as well as between the bound electrons induced by the blackbody radiation (BBR). All the derivations are given within the rigorous QED theory. It is shown that these thermal corrections are the same order in powers of a (fine-structure constant) as the well-known BBR-induced Stark shift but different behavior in temperature. The numerical results presented in this paper make it possible to expect their significance for modern experiments and testing the fundamental interactions in helium.