A Markov chain model is proposed for modelling residence time distribution of a tracer flowing together with a polymer through a single screw extruder, which has been designed for polymer extrusion with injection of supercritical CO2. The model has two dimensions and takes into consideration different velocity profiles of the flowing polymer between the screw and the barrel wall. In addition, the model allows obtaining the system response on any testing signal as unit step, Dirac or sinusoidal functions. In this work, the influence of the barrel temperature is considered. Experimental results of residence time distribution are given at different temperatures. A procedure of the model parameter identification from experiments was proposed. Within the range of working temperatures tested, a linear dependence of the velocity profile parameters was used to fit the experimental and model data.