  Using the Feynman-Pines diagram technique, the energy spectrum of localized
quasi-particles interacting with polarization phonons is calculated and
analyzed in the wide range of energies at the finite temperature of the system.
It is established that the general model of the system, besides the bound
states known from the simplified model with an additional condition for the
operator of quasi-particles number, contains the new bound states even for the
systems with weak coupling. The contribution of multi-phonon processes into the
formation of renormalized spectrum of the system is analyzed. The reasons of
the appearance, behaviour and disappearance of separate pairs of bound states
depending on the coupling constant and temperature are revealed.
