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 _ { \odot } } .
In gas with a metallicity { Z } = 0.1 \ > { Z _ { \odot } } , and in the absence of an incident ultraviolet radiation field , it is valid for hydrogen number densities n _ { H } \mathbin { \lower 3.0 pt \hbox { $ \hbox to 0.0 pt { \raise 5.0 pt \hbox { $ \char 6 % 0 $ } } \mathchar 29208 $ } } 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 } \ll 0.1 \ > { Z _ { \odot } } , 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 .