Using temperature modulated differential scanning calorimetry (TM-DSC) the complex frequency dependent heat capacity C(omega) can be measured. C(omega) is connected to an additional time dependent variable zeta(t), which describes the kinetics of processes inside the sample. Usage of phenomenological or molecular models for C(t) allows the interpretation of measured TM-DSC curves. This is illustrated for the melting of Poly(ethylene terephthalate) (PET) and Poly(E-caprotactone) (PCL).The melting of polymers is investigated and compared to a first- and second-order phase transition. The behaviour of the complex heat capacity in the melting region of polymers is manifold. Using different empirical models for the local melting and relaxation process in the melt the quantitative behaviour of the measured curves can be described.