The effect of resonant inverse Compton scattering on gap formation above pulsar polar caps is investigated. Soft photons due to thermal emission from the polar cap can be Compton scattered to very high energies by primary particles accelerated in the polar cap region. These Compton-scattered photons can initiate a pair cascade, which then limits the height of the acceleration zone (i.e., the gap thickness). The gap model including the effect of resonant inverse Compton scattering is applied to pulsars with strong magnetic fields (≥ 1012 G). It is found that when magnetic fields are sufficiently strong and the polar cap is sufficiently hot, the thickness of the gap is limited by a pair cascade triggered by resonant Compton-scattered photons to a value that can be much smaller than that derived by considering only curvature photon-initiated pair cascade. Conditions under which such Compton scattering has important effects on polar gap formation are derived. The hot polar cap may be the result of polar cap heating due to a reverse particle flux. A fraction of secondary positrons (or electrons if free emission of ions is assumed) is accelerated back to the polar cap, resulting in self-sustained polar cap heating.