The new capabilities of AC calorimetry, when working at frequencies above the classical limit were demonstrated. The appropriate frequency range of classical AC calorimetry was substantially enlarged. It was shown that the advanced AC calorimetry can be applied for studying dynamic heat capacity of polymers in the frequency range 0.1-1 Hz. Thus, the processes with characteristic time as short as ca. 5 s was registered. The advanced AC technique was applied for investigation of the melting kinetics in polycaprolactone. It was found that melting in polycaprolactone is related to an activated process. The activation of the melting process after a step heating is described by a stretched exponent and the decay of the melting by only one exponent at short times. The dependencies of the exponent on temperature and thermal treatment were investigated at frequencies in the range 0.1-1Hz and modulation amplitudes 0.005-0.2 K.