  I explore the thermal evolution and ionization states in gas cooling from an
initially hot state in the presence of external photoionizing radiation. I
compute the equilibrium and nonequilibrium cooling efficiencies, heating rates,
and ion fractions for low-density gas cooling while exposed to the ionizing
metagalactic background radiation at various redshifts (z=0 - 3), for a range
of temperatures (1e8-1e4 K), densities (1e-7 - 1e3 cm^-3) and metallicities
(1e-3 - 2 times solar). The results indicate the existence of a threshold
ionization parameter, above which the cooling efficiencies are very close to
those in photoionization equilibrium (so that departures from equilibrium may
be neglected), and below which the cooling efficiencies resemble those in
collisional time-dependent gas cooling with no external radiation (and are thus
independent of density)
