At present, a fundamental knowledge of the thermal and mechanical interactions occurring during the extrusion of magnesium is lacking. This acts as a serious technological barrier to the cost-effective manufacturing of lightweight magnesium alloy profiles. In the present research, a three-dimensional finite element (FE) simulation of extrusion to produce a magnesium alloy profile with a cross shape was carried out as an efficient means to gain this understanding. It revealed the redistribution of temperatures in the billet throughout the process from the transient state to the steady state, the formation of the deformation zone and dead metal zone, and varying fields of effective stress, effective strain, effective strain rate, and temperature close to the die orifice. The predicted extrudate temperature and extrusion pressure were compared with experimental measurements. The key to controlling the extrudate temperature and extrusion process was found to lie in the capabilities of predicting the temperature evolution during transient extrusion, as affected by extrusion conditions. The relationship between ram speed and the extrudate temperature increase from the initial billet temperature was established and experimentally validated.