Welding of dissimilar materials is critical in industries where mixed materials with high strength-to-weight ratios are urgently needed. Friction element welding (FEW) is a promising solution, with the ability to join high-strength materials for a wide range of thicknesses with low input energy and a short processing time. However, the temperature evolution and the influence of different processing parameters remain unclear. To bridge this knowledge gap, this work develops a coupled thermal-mechanical finite element model to study the FEW process. The simulation results agree well with the experimental measurements of material deformation and transient temperature evolution. It is found that the friction element's rotational speed has the greatest impact on friction heat generation, followed by the processing times for different steps. The aluminum layer is heated during the penetration and cleaning steps, thus a lower rotational speed during the penetration step can help prevent the aluminum layer from undesired overheating. The steel layer and the friction element are mainly heated during the cleaning and welding steps. The strong heating, potentially melting, will be beneficial to the friction element's plastic deformation and bond formation. To enhance the heating of the steel layer and the friction element, faster rotational speeds or longer processing periods could be employed during the cleaning and welding steps. The results by this study establish the relationship between processing conditions and the temperature evolution of different parts, which will guide the design and optimization of the FEW technique for various applications.