  We investigate the effect of pulsar polar cap (PC) heating produced by
positrons returning from the upper pair formation front. Our calculations are
based on a self-consistent treatment of the pair dynamics and the effect of
electric field screening by the returning positrons. We calculate the resultant
X-ray luminosities, and discuss the dependence of the PC heating efficiencies
on pulsar parameters, such as characteristic spin-down age, spin period, and
surface magnetic field strength. In this study we concentrate on the regime
where the pairs are produced in a magnetic field by curvature photons emitted
by accelerating electrons. Our theoretical results are not in conflict with the
available observational X-ray data and suggest that the effect of PC heating
should significantly contribute to the thermal X-ray fluxes from middle-aged
and old pulsars. The implications for current and future X-ray observations of
pulsars are briefly outlined.
