A Cooling Function is a function of Temperature indicating the rate that a gas cools, more specifically, giving the rate it cools divided by the Number Density of gas Particles squared.
R = n²Λ(T)
Such functions are used in modeling the cooling of gas clouds into galaxies or Protostars. A specific function is based upon the constitution of the gas. The functions presume the gas's Optical Depth is much less than one (Optically Thin), i.e., a Photon emitted will generally leave the cloud.
The function generally has multiple peaks and valleys due to the varied Emission mechanisms that are most efficient at particular temperatures. The mechanisms are the same as those in Radiative Transfer, e.g., within stars, the difference being the optical thinness.