In this article, a numerical solution of a system of differential equations is proposed, able to describe the kinetic curing of a polyester resin in a temperature range between 336 K up to 363 K. The conversion degree of both styrene and polyester unsaturations were experimentally measured, in a preceding article, by Fourier Transform Infrared Spectroscopy; now we describe a more precise and correct theoretical calculation of the kinetic reactions relative to the experiments described in that; previous article. This new calculation is based on the solution of the kinetic equations, based on free radicals polymerization reaction, instead of empirical formulas. The obtained results, relative to the conversion degree of both the components, show better agreement with the experimental values, both with respect to the usual kinetic model and also compared with a new empirical model that we proposed in the previous article, to fit the same set of experimental data. The comparison between the models was performed by hypothesis test. The parameters that characterize the propagation reactions were found to increase with increasing temperature, according to an Arrhenius law, leading to an activation energy between (98 +/- 2) KJ/mol for the styrene and (110 +/- 2) KJ/mol for polyester unsaturation, in the temperature range examined. We conjecture this system could be useful to monitor for each time, the consumption of the different species present in the kinetic reaction, and to refine the final thermo-mechanical properties of the resins.