The thermal relaxation times of thin indium and lead films evaporated on sapphire and quartz single-crystal substrates have been measured. These times are compared with the predictions of two models for the heat-loss process. The first assumes perfect thermal contact between the two materials and corresponds to perfect black-body phonon radiation from the film into the insulator. The second, which predicts a somewhat reduced rate of heat loss (up to ∼40% less), corresponds to an acoustic-mismatch model in which the reflection of phonons at the interface is considered. The possible relevance of these two models to the experimental situation in which a metal film is involved is discussed. Experimentally it is found that the results for the indium films approach the predictions for the perfect-thermal-contact model, while the results for the lead films show a slower rate of heat loss than either model predicts. Comparison to other experimental results is also made. © 1966 The American Physical Society.