The glass transition can be measured at different experimental conditions. Using spectroscopic methods at relative high frequency the a-relaxation is measured in the thermodynamic equilibrium. In the caloric ease we call this phenomenon thermal relaxation transition (TRT). With a conventional differential scanning calorimeter (DSC) the transition of the equilibrium (the melt) into a nonequilibrium (the glassy state) is measured. This effect is called thermal glass transition (TGT). In contrast to the TGT, the TRT can be described using the linear response approach. The temperature-modulated differential scanning calorimetry (TIMDSC) technique superimposes a periodical temperature perturbation upon the constant scanning rate of conventional DSC. This technique combines a spectroscopic method with a linear temperature scan. Both the TGT and the TRT are measured simultaneous. Because the frequencies are relatively low in a TMDSC experiment, the temperature ranges of both transitions overlap. In this case, the experimental results show an influence of the TGT on the TRT. The reason of that is the deviation from the nonequilibrium. In this case, the fictive temperature is different from the external temperature. This effect can be described by me ans of a Tool-Narayanaswamy-Moynihan model for the TGT. Based on this model, a description of the complex heat capacity close to the thermal glass transition is shown. The influence of the beginning freezing-in process on the thermal relaxation is characterized by the fictive temperature. Using the presented description, a quantitative calculation of the nonlinear effects in the thermal relaxation is possible.