A consistent description of temperature modulated differential scanning calorimeter (TM-DSC) curves based on irreversible thermodynamics is presented within the scope of the validity of the linear response approximation. Both time-independent and time-dependent processes are included. For time-dependent (linear) processes, the heat how rate is connected to the convolution integral. This results in a generalized heat capacity which is frequency dependent and, on principle, a complex function of it.