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The extrusion process is one of the main methods of processing polymeric materials and thermal homogeneity of the process output presents a major challenge for high quality extruded products. Therefore, accurate process thermal monitoring and control are highly desirable. However, most of the industrial extruders use conventional single point thermocouples for thermal monitoring although their measurements are highly affected by barrel metal wall temperature. Moreover, it has been shown that the melt temperature changes considerably with the die radial position and point based measurements are not sufficient to determine the actual process thermal stability and hence to control the thermal homogeneity of melt output. Conversely, the majority of process thermal control methods are based on linear models and are not capable of dealing with process nonlinearities. In this work, a die melt temperature profile was monitored by a thermocouple mesh technique and the data obtained was used to formulate a new nonlinear dynamic model to predict the die melt temperature profile in a single screw extruder. The model is in good agreement with the measured data and offers a promising thermal monitoring technique which can be used in real-time for a thermal profile based control framework in polymer extrusion.