We study the frequency response of a micro calorimeter implementing an oscillating temperature regime. The micro calorimeter combines a free-standing membrane together with lithographic techniques that allow to fit the sample-holder to be adapted to samples of a few micrograms. We show that the conventional model of Sullivan and Seidel is inaccurate due to of the contributions of the addenda contributions. We propose an error function that takes into account the influence parameters of the four body sample-holder (sample, membrane, sensors and gold isotherm). By minimizing the error function, we propose conditions to adjust the frequency domain measurement in order to improve the accuracy of the heat capacity measurements.