3D computer simulations of extruding a wrought magnesium alloy AZ31 into a rectangular section at various ram speeds were performed and the results verified in extrusion experiments under identical conditions. It has been found that during upsetting and transient-state extrusion, the temperature in the billet is redistributed all over; it increases in the deformation zone close the die orifice and decreases in the rear part of the billet. The maximum temperature is located at the centre of the outer surface of the extruded section where more heat is generated and less heat lost. The minimum temperature occurs at the edge of the billet in contact with the container and the die face where the dead metal zone is situated. During upsetting and transient-state extrusion, the maximum temperature increases significantly, while during steady-state extrusion it only changes slightly. The amplitude of the extrudate temperature increase from the initial billet temperature during steady-state extrusion at a given ram displacement decreases as ram speed increases. Thus, the higher ram speed, the smaller the effect of ram speed on temperature increase. The increase of the extrudate temperature varies linearly with logarithmic ram speed.With this relationship established, the extrudate temperature at different ram speeds can conveniently be predicted.