In the second part of this paper devoted to the problem of the thermal self-focusing of an electromagnetic wave in an underdense plasma, we extend the linear theory of part 1 to include the effect of collisional energy transfer from the electrons to the ions. The eigenvalue problem which gives the spectrum of the wave modes that occur in a beam of finite width is formulated and solved for the case of a square beam profile. From the resulting dispersion relation, we derive the unstable wavenumber band and the maximum spatial growth rate. An approximate solution of the dispersion relation is obtained for the case of a thin beam which illustrates how the stabilizing influence of energy transfer to the ions affects the unstable spectrum. In addition, some numerical solutions of the dispersion relation are presented for the cases of ionospheric modification by a power satellite microwave beam and by an ionospheric HF heater.