A computer system is developed to quantitatively reveal how the melt temperature is affected by the operating conditions during the plastication, dwell and injection stages of the injection molding process. The variables considered in this study are rotation speed, back pressure, barrel heater temperatures, nozzle heater temperature, dwell time and injection velocity profile. A set of Artificial Neural Networks (ANN) has been developed to predict the effect of the operating conditions on the melt temperature during plastication. The dwell period is treated as a heat conduction problem. A free boundary model for the injection phase is developed to simulate the temperature development and melt flow due to the forward motivation of the screw. The overall prediction of nozzle melt temperature is in good agreement with the experimental measurement, validating the proposed procedure combining ANNs and mathematical modeling. This work enhances the understanding of the process and provides a basis for future work on the optimization and advanced control of the process.