Because of the nonlinear change in the properties of a material with change in temperature, sinusoidal temperature modulation will alter the magnitude of a measured property and the rate of an irreversible transformation. These effects are mathematically described and elaborated. From real-time dielectric spectroscopy and calorimetric measurements performed on a model liquid undergoing stepwise network structure polymerization until its vitrification, it is shown that the effects of sinusoidal temperature modulation are substantial, and need to be considered in the analysis of the data. Features that appear in the plots against time vanish in plots against the extent of polymerization, an intrinsic property. Fourier transform of the heat flow in response to a sinusoidal temperature modulation may help determine the magnitude of this effect in the form of second or higher order harmonic terms. This in turn may be used to calculate the temperature and time dependence of the nonlinear effects. These fundamental aspects will be useful for the current efforts in incorporating sinusoidal temperature modulation in calorimetry.