The later stages of cooling of molecules and clusters in the interstellar medium are dominated by emission of vibrational infrared radiation. With the development of cryogenic storage it has become possible to experimentally study these processes. Recent storage ring results demonstrate that intramolecular vibrational redistribution takes place within the cooling process, and an harmonic cascade model has been used to interpret the data. Here we analyze this model and show that the energy distributions and the photon emission rates develop into near-universal functions that can be characterized with only a few parameters, irrespective of the precise vibrational spectra and oscillator strengths of the systems. We show that the photon emission rate and emitted power vary linearly with total excitation energy with a small offset. The time developments of ensemble internal energy distributions are calculated with respect to their first two moments. The excitation energy decreases exponentially with a rate constant which is the average of all k1→0 Einstein coefficients, and the time development of the variance is also calculated.