  Thermal corrections to the one-photon spontaneous and induced transition
probabilities for hydrogen and hydrogen-like ions are evaluated. The found
thermal corrections are given by the vertex Feynman graph, where the vertex
represents the thermal interaction between the bound electron and the nucleus.
All derivations of thermal corrections to bound-bound transitions for an atom
exposed to blackbody radiation (BBR) are made in a fully relativistic approach
within the framework of the adiabatic $S$-matrix formalism. It is found that
the vertex-type radiative corrections to the transition rates can be at the
level of a few percent to corresponding spontaneous rates for highly excited
states in the hydrogen atom. A comprehensive analysis of the vertex-type
thermal corrections for hydrogen-like atomic systems is presented.
