The model of energy transfer in collisions of atoms with vibrationally excited polyatomic molecules suggested recently by the present authors (J. Phys. Chem. 1993, 97, 9397) and based on consecutive direct encounters is generalized. Incorporation of the lifetime distribution of collisions into the Landau-Teller model of the description of the energy transfer in a single encounter yields a general formula for the temperature dependence of the mean energy, [Delta E], transferred in a collision. This formula takes into account the interplay between the positive temperature dependence originating from the energy-gap law and the negative temperature dependence which is related to the collision lifetime. Good agreement of the temperature dependence of [Delta E] between the present model and trajectory calculations is obtained.