Recombination cooling, in which a free electron emits light while being captured to an ion, is an important cooling process in photoionized clouds that are optically thick or have low metallicity. State specific rather than total recombination cooling rates are needed since the hydrogen atom tends to become optically thick in high-density regimes such as Active Galactic Nuclei. This paper builds upon previous work to derive the cooling rate over the full temperature range where the process can be a significant contributor in a photoionized plasma. We exploit the fact that the recombination and cooling rates are given by intrinsically similar formulae to express the cooling rate in terms of the closely related radiative recombination rate. We give an especially simple but accurate approximation that works for any high hydrogenic level and can be conveniently employed in large-scale numerical simulations. LaMothe, J. and Ferland, Gary J. Goddard Space Flight Center ...