The time development of the excitation energy of molecules and clusters cooling by emission of thermal vibrational infrared radiation has been studied. 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. The photon emission constant and emitted power averaged over all thermally populated states 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. For the derived linear dependence of the emission rate constant, these results are exact.