  Temperature Modulated calorimetry is widely used but still raises some
fundamental questions. In this paper we study a model system as a test sample
to address some of them. The model has a nontrivial spectrum of relaxation
times. We investigate temperature modulated calorimetry at constant average
temperature to precise the meaning of the frequency-dependent heat capacity,
its relation with entropy production, and how such measurements can observe the
aging of a glassy sample leading to a time-dependent heat capacity. The study
of the Kovacs effect for an out-of-equilibrium system shows how temperature
modulated calorimetry could contribute to the understanding of this memory
effect. Then we compare measurements of standard scanning calorimetry and
temperature-modulated calorimetry and show how the two methods are
complementary because they do not observe the same features. While it can probe
the time scales of energy transfers in a system, even in the limit of low
frequency temperature modulated calorimetry does not probe some relaxation
phenomena which can be measured by scanning calorimetry, as suggested by
experiments with glasses.
