  The thermal two-photon level broadening of the excited energy levels in the
hydrogen and H-like helium is evaluated via the imaginary part of thermal
two-loop self-energy correction for bound electron. All the derivations are
presented in the framework of rigorous quantum electrodynamic theory at finite
temperatures and are applicable for the H-like ions. On this basis, we found a
contribution to the level broadening induced by the blackbody radiation which
is fundamentally different from the usual line broadening caused by the
stimulated two-photon decay and the Raman scattering of thermal photons.
Numerical calculations of the two-loop thermal correction to the two-photon
width for the $2s$ state in hydrogen and singly ionized helium atoms show that
the effect could significantly exceed the higher-order relativistic and
radiative QED corrections commonly included in the calculations. In addition,
the thermal two-loop self-energy correction significantly exceeds the
"ordinary" stimulated one-photon depopulation rate at the relevant laboratory
temperatures. In this work, detailed analysis and the corresponding comparison
of the effect with the existing laboratory measurements in H-like ions are
carried out.
