The temperature dependence of the pure vibrational dephasing rate in two different model heteropolymers is examined. One model is an anharmonic chain of atoms coupled by random forces, for which the pure dephasing rate of one mode is calculated. The second is a CO ligand coupled to an alpha-helix of the protein myoglobin. In both models the rate of pure dephasing due to coupling to vibrational modes of the heteropolymer is found to obey an apparent power-law temperature dependence T-alpha, alpha approximate to 1.3-1.4, over the temperature range of the calculations, from well below 100 to about 200 K. (C) 2002 Elsevier Science B.V. All rights reserved.