Hot tearing is a well-known limitation when trying to maximize the throughput rate in aluminium extrusion. In the present work an analytical modelling framework is presented which can be used to predict the maximum extrusion speed that can be applied in production without formation of this type of surface defect. The modelling framework allows almost instantaneous estimates on the resulting productivity in terms of maximum extrusion speed. This is obtained by developing an analytical model for the maximum temperature at the die exit which incorporate the effect of alloy composition and billet processing. The results are consolidated into extrusion limit diagrams, mapping the maximum allowable extrusion speed as a function of billet pre-heat temperature, alloy composition, and homogenisation heat treatment. The calculated temperatures and extrusion limit diagrams obtained from the analytical model are compared with measured temperatures and critical extrusion speeds from extrusion tests of various 6xxx series alloys for a simple rod-shaped geometry. The comparisons indicate that the presented modelling approach gives sufficiently accurate predictions for future application in optimisation of alloy composition and process parameters in extrusion of profiles.