  We use a non-equilibrium chemical network to revisit and study the effect of
H_{2}, HD and LiH molecular cooling on a primordial element of gas. We solve
both the thermal and chemical equations for a gas element with an initial
temperature T\approx 1000K and a gas number density in the range
n_{tot}=1-10^{4} cm^{-3}. At low densities, n_{tot}<10^{2} cm^{-3}, the gas
reaches temperatures \sim 100K and the main coolant is H_{2}, but at higher
densities, n_{tot}>10^{2} cm^{-3}, the HD molecule dominates the gas
temperature evolution. The effect of LiH is negligible in all cases. We studied
the effect of D abundance on the gas cooling. The D abundance was set initially
to be in the range n_{D}/n_{H}=10^{-7}-10^{-4.5}, with
n_{HD}/n_{H}={D^{+}}/n_{H}=10^{-10}. The simulations show that at
n_{tot}>10^{2} cm^{-3} the HD cooling dominates the temperature evolution for D
abundances greater than 10^{-5}n_{H}. This number decrease at higher densities.
Furthermore, we studied the effect of electrons and ionized particules on the
gas temperature. We followed the gas temperature evolution with
n_{H_{+}}/n_{H}=10^{-4}-10^{-1} and n_{D^{+}}/n_{H^{+}}=10^{-5}. The gas
temperature reached lower values at high ionization degree because electrons,
H^{+} and D^{+} are catalizers in the formation paths of the H_{2} and HD
molecules, which are the main coolers at low temperatures. Finaly, we studied
the effect of an OB star, with T_{eff}=4\times 10^{4}K, would have on gas
cooling. It is very difficult for a gas with n_{tot} in the range between 1-100
cm^{-3} to drop its temperature if the star is at a distance less than 100 pc.
