  We investigate a model of galaxy clusters in which the hot intracluster gas
is efficiently heated by dynamical friction (DF) of galaxies. We allow for both
subsonic and supersonic motions of galaxies and use the gravitational drag
formula in a gaseous medium presented by Ostriker (1999). The energy lost by
the galaxies is either redistributed locally or into a Gaussian centered on the
galaxy. We find that the condition of hydrostatic equilibrium and strict energy
balance yields a trivial isothermal solution T_iso, independent of radius, or
rising temperature distributions provided T_iso/gamma < T < T_iso, where gamma
is the adiabatic index of the gas. The isothermal temperature corresponds to
the usual scaling relation between the gas temperatures and the velocity
dispersions of galaxies. However the minimal temperature associated with the
rising solutions is ~ 0.5 T_vir, larger than that inferred from observations,
the radial distribution of galaxy masses notwithstanding. Heating by
supersonically moving galaxies cannot suppress thermal instability, although it
can lengthen the growth time up to the level comparable to the ages of clusters
when Mach number of galaxies is less than about two. We show using numerical
hydrodynamic simulations that DF-induced heating is generally unable to produce
stable equilibrium cores by evolving arbitrary non-equilibrium clusters,
although it can lengthen the cooling time. We conclude that DF-induced heating
alone is an unlikely solution to the cooling flow problem, although it can
still be an important heat supplier, considerably delaying cooling catastrophe.
We discuss other potential consequences of DF of galaxies in galaxy clusters.
