For complex heat capacity measurements, various types of temperature modulated differential scanning calorimetry (tm-DSC) can be used. However, three factors have influence on steady state of tm-DSC and hence cause errors in complex heat capacity measurements. These factors are heat capacities along heat paths in the instrument, temperature distribution within the sample, and thermal contact among the sample, the sample cell and its holder plate. They are theoretically investigated by a set of comprehensive fundamental equations of heat balance based on a common model applicable to all existing types of tm-DSC. For heat paths in the instrument, heat loss to the environment and mutual heat exchange between the sample and the reference material are also taken into accounts, beside the main heat flows from the heat sources to the sample and the reference material. Rigorous and general solutions have been obtained, and useful relations for complex heat capacity measurements have been derived for each type of tm-DSC. Examining the solutions, new insight into tm-DSC is obtained, and errors and their correction are discussed. They are characteristic of tm-DSC types and compared with each other.