Irreversible melting of poly(ethylene terephthalate) crystals on heating has been examined by temperature modulated differential scanning calorimetry (t.ms.c.). The apparent heat capacity of complex quantity obtained by t.ms.c. showed a strong dependence on frequency and heating rate during the melting process. In order to explain this behavior, a kinetic modelling of melting has been presented. The modelling considers the melting of an assembly of fractions having a continuous distribution of non-equilibrium melting points. Three cases of the superheating dependence of melting rate coefficient have been examined : constant rate coefficient, linear dependence and exponential dependence. The modelling predicts frequency response functions similar to Debye＇s type with a characteristic time dependent on heating rate. The response function successfully explains the dependence on frequency and heating rate of the apparent heat capacity obtained experimentally. The characteristic time of melting of crystallites has been evaluated as a fitting parameter of the response function, and the superheating dependence of melting rate coefficient has been distinguished by the heating rate dependence of the characteristic time. Taking account of the relatively insensitive nature of crystallization to temperature modulation, it is further suggested that the ＇reversing＇ heat Bow is related to the pure endothermic heat flow of melting and the ＇non-reversing＇ heat flow corresponds to the exothermic heat flow of re-crystallization and reorganization when extrapolated to omega --> 0. The behavior of the apparent heat capacity will be an important characteristic feature of the melting kinetics, and hence the modelling will develop a new applicability of t.ms.c. to the melting of polymer crystals.