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Extensive line lists generated as part of the ExoMol project are used to compute lifetimes for individual rotational, rovibrational and rovibronic excited states, and temperature-dependent cooling functions by summing over all dipole-allowed transitions for the states concerned. Results are presented for SiO, CaH, AlO, ScH, H_2O and methane. The results for CH_4 are particularly unusual with 4 excited states with no dipole-allowed decay route and several others where these decays lead to exceptionally long lifetimes. These lifetime data should be useful in models of masers and estimates of critical densities, and can provide a link with laboratory measurements. Cooling functions are important in stellar and planet formation.