Single-screw plastication, used in extrusion and in injection moulding, is a major way of processing commodity thermoplastics. During the plastication phase, the polymeric material is melted by the combined effects of shear-induced self-heating (viscous dissipation) and heat conduction coining from the barrel. In injection moulding, a high level of reliability is usually achieved that makes this process ideally suited to mass market production. Nonetheless, process fluctuations still appear that make moulded part quality control an everyday issue. In this work, we used a combined modelling of plastication, throughput calculation and laminar dispersion, to investigate if, and how, thermal fluctuations could propagate along the screw length and affect the melt homogeneity at the end of the metering section. To do this, we used plastication models to relate changes in processing parameters to changes in the plastication length. Moreover, a simple model of throughput calculation is used to relate the screw geometry, the polymer rheology and the processing parameters to get a good estimate of the mass flow rate. Hence, we found that the typical residence time in a single screw is around one tenth of the thermal diffusion time scale. This residence time is too short for the dispersion coefficient to reach a steady state, but too long to be able to neglect radial thermal diffusion and resort to a purely convective solution. Therefore, a full diffusion/convection problem has to be solved with a base flow described by the classic pressure and drag velocity field. Preliminary results already show the major importance of the processing parameters in the breakthrough curve of an arbitrary temperature fluctuation at the end of the metering section of injection moulding screw. When the flow hack-pressure is high, the temperature fluctuation is spread more evenly with time, whereas a pressure drop in the flow will results in a breakthrough curve which presents a larger peak of fluctuation.