  We model the photoelectric emission from and charging of interstellar dust
and obtain photoelectric gas heating efficiencies as a function of grain size
and the relevant ambient conditions. Using realistic grain size distributions,
we evaluate the net gas heating rate for various interstellar environments, and
find less heating for dense regions characterized by R_V=5.5 than for diffuse
regions with R_V=3.1. We provide fitting functions which reproduce our
numerical results for photoelectric heating and recombination cooling for a
wide range of interstellar conditions. In a separate paper we will examine the
implications of these results for the thermal structure of the interstellar
medium. Finally, we investigate the potential importance of photoelectric
heating in H II regions, including the warm ionized medium. We find that
photoelectric heating could be comparable to or exceed heating due to
photoionization of H for high ratios of the radiation intensity to the gas
density. We also find that photoelectric heating by dust can account for the
observed variation of temperature with distance from the galactic midplane in
the warm ionized medium.
