  We present a simplified chemical and thermal model designed to allow
computationally efficient study of the thermal evolution of metal-poor gas
within large numerical simulations. Our main simplification is the neglect of
the molecular chemistry of the heavy elements. The only molecular chemistry
retained within the model is the formation and destruction of molecular
hydrogen. Despite this major simplification, the model allows for accurate
treatment of the thermal evolution of the gas within a large volume of
parameter space. It is valid for temperatures 50 < T < 10000 K and
metallicities 0 < Z < 0.1 Z_solar. In gas with a metallicity Z = 0.1 Z_solar,
and in the absence of an incident ultraviolet radiation field, it is valid for
hydrogen number densities n_H < 500 / t_char cm^-3, where t_char is the size in
Myr of the characteristic physical timescale of interest in the problem. If Z
<< 0.1 Z_solar, or if a strong ultraviolet radiation field is present, then the
model remains accurate up to significantly higher densities. We also discuss
some possible applications of this model.
