In this paper, computer simulations were performed on the extrusion of 7075 aluminium billets with non-uniform temperature distributions in order to inhibit excessive temperature rise that tends to occur during the conventional extrusion of a uniformly preheated billet. The simulations showed that when a linear temperature distribution was imposed on a billet with its rear end 150°C colder than its front end, the maximum temperature of the workpiece would still increase from 450°C to over 520°C at the end of an extrusion cycle, giving rise to hot shortness. Assigning a non-linear temperature distribution during preheating the billet could however significantly lessen this undesirable temperature increase, leading to isothermal extrusion. Such a non-linear temperature distribution was determined on the basis of the results obtained from the simulation of the extrusion of a billet with a linear temperature distribution. With this predetermined non-linear temperature distribution, the maximum temperature of the workpiece remained stable near the die entrance. The radial temperature variation on the cross-section of the extrudate became less significant as the material flowed through the die. In addition, the simulations showed another advantage of isothermal extrusion, i.e. an invariable die face pressure throughout an extrusion cycle. The maximum positive (tensile) principle stress was revealed at the corner of the die orifice, indicating that tearing tended to occur there.