The modeling of bubble growth was employed as a technique to control the cellular structure and by taking the equations of bubble growth and rubber curing into account simultaneously, the instantaneous radius of cells as a function of time was predicted. Side-by-side solves of the Kamal-Sourour kinetic model, as well as the heat transfer equation, led to the development of temperature variation function. Also, the predictions of the employed model concerning the effects of different parameters like the temperature of the foaming process, the level of foaming agent, and various physical attributes such as viscosity, gas diffusion coefficient, thermal conductivity, density, and surface tension on the bubble growth and radius alterations were analyzed. Based on the obtained scanning electron microscopy image from the cellular structure, there was only a 15% disparity between the predicted and experimental data about the bubble radius. Contrary to temperature, viscosity, and thermal conductivity, an increment in the level of foaming agent, diffusion coefficient, and density caused a rise of bubble radius. Also, the surface tension had an insignificant impact on the volume of the bubbles. Based on the findings, the applied model has proper credibility and can predict the influences of the abovementioned factors with satisfying accuracy.