The long time scale evolution, that is, for times long compared to an electron collision period of high-power radio wave ionospheric heating, is studied. Preliminary studies are made to model high-power radio wave propagation in an ionosphere containing a dynamically produced electron density cavity. We show that high-power radio wave-induced plasma density depletions in the F region ionosphere will convect and steepen in the direction perpendicular to the geomagnetic field due to ionosphere-thermosphere coupling effects. We treat high-power radio wave propagation including nonlinear self-induced thermal effects in presence of a steepened density depletion. We find that the beam is distorted, shifts in direction, and changes its peak intensity due to nonlinear self-induced thermal effects. For weak beams, we find a decrease in beam intensity while for strong beams we observe an increase in beam intensity.