  X-ray observations of hot gas in galaxy groups indicate higher entropies than
can be achieved in the accretion shocks as it fell into the dark halos. It has
been proposed that this entropy excess results from some universal external
heating process in the early universe - AGN, population III stars, etc. - that
occurred before most of the gas entered the dark halos. Alternatively, the hot
gas in groups may be heated internally by Type II supernovae when the galactic
stars formed. We investigate here the gas-dynamical consequences of various
amounts of external, high redshift heating and compare with internal supernova
heating. Radiative losses and distributed mass dropout are included. We find
that externally heated flows are unsatisfactory; when the heating is high
enough to bring the X-ray luminosities into agreement with observations, the
gas entropy is too high. Flows internally heated by Type II supernovae are
preferred. Our results are insensitive to the epoch and spatial distribution of
the supernova heating process. However, with a Salpeter IMF a large fraction of
the energy produced by supernovae must heat the hot gas. Alternatively, only
about 20 percent of the Type II supernova energy would be required to heat the
gas if the initial mass function is flatter than Salpeter, as suggested by
stellar mass to light ratios.
