Complex reactions taking place between Ca3SiO5 and water can be considered the main cause for setting and hardening of Portland cement pastes. The "in situ" kinetics of the "hydration" process has been recently studied, as a function of time, using neutron scattering to obtain the trend of the fraction of free water (free water index, FWI), i.e., the fraction of unreacted water. In this study we developed a novel and simple approach on the basis of differential scanning calorimetry to follow the hydration kinetics of Ca3SiO5 in real, time from the decrease of the free water index. FWI has been obtained by measuring the fraction of water in the Ca3SiO5 paste that can solidify and melt. We report the trend of FWI as a function of Ca3SiO5 paste hydration and the results are compared to recent quasi-elastic neutron scattering experiments. The results account well for the hydration process described by two kinetic stages, the first according to an Avrami-Erofeev nucleation and growth law, and the second one to a three-dimensional diffusion equation. Activation energies and rate constants were also computed. Moreover, the hydration process was followed in the presence of an organo-aza-phosphonate additive, which is known to inhibit nucleation and growth of solid phases from aqueous media. We found that this additive is very powerful in retarding the hydration process even at very low concentration, by increasing the activation energy, of the Avrami-Erofeev stage. Although quasi-elastic neutron scattering and NMR are more powerful and provide additional information on the water dynamics, we believe that this new simple method will become very popular in all applied investigations, where the knowledge of FWI is essential.