  The theory of renormalized energy spectrum of localized quasi-particle
interacting with polarization phonons at finite temperature is developed within
the Feynman-Pines diagram technique. The created computer program effectively
takes into account multi-phonon processes, exactly defining all diagrams of
mass operator together with their analytical expressions in arbitrary order
over the coupling constant. Now it is possible to separate the pole and
non-pole mass operator terms and perform a partial summing of their main terms.
The renormalized spectrum of the system is obtained within the solution of
dispersion equation in the vicinity of the main state where the high- and
low-energy complexes of bound states are observed. The properties of the
spectrum are analyzed depending on the coupling constant and the temperature.
