A Hamiltonian for the electron-phonon system in the double-well resonant tunneling structure in the dc electric field has been obtained, by using the models of rectangular potential profile and effective mass for electrons and the dielectric continuum model for phonons. This structure is a separate cascade of the injectorless quantum cascade laser. The renormalized parameters of the electron spectrum are calculated for an arbitrary temperature, by using the method of thermodynamic Green's functions. It is shown that, in accordance with the experiment, the laser radiation band broadens out and weakly shifts with the temperature growth. K e y w o r d s: resonant tunneling nanostructure, quantum cascade laser, interface phonons, electron-phonon interaction, Green's function.