The heat capacity of poly[carbonyl(ethylene-co-propylene)] with 95 mol % C2H4-CO- (Carilon EP (R)) was measured with standard differential scanning calorimetry (DSC) and temperature-modulated DSC (TMDSC). The integral functions of enthalpy, entropy, and free enthalpy were derived. With quasi-isothermal TMDSC, the apparent reversing heat capacity was determined from 220 to 570 K, including the glass- and melting-transition regions. The vibrational heat capacity of the solid and the heat capacity of the liquid served as baselines for the quantitative analysis. A small amount of apparent reversing latent heat was found in the melting range, just as for other polymers similarly analyzed. With an analysis of the heat-flow rates in the time domain, information was collected about latent heat contributions due to annealing, melting, and crystallization. The latent heat decreased with time to an even smaller but truly reversible latent heat contribution. The main melting was fully irreversible. All contributions are discussed in the framework of a suggested scheme of six physical contributions to the apparent heat capacity.