Dissimilar material welding has gradually become the focus of industrial applications, and the selection principle of dissimilar welding process parameters has been increasingly considered; thus, providing an accurate and reliable welding parameter selection principle is more important. On the basis of the Onsager-Ziegler maximum entropy generation principle (OZ-MEPP) and related dynamics principles, a steady-state one-dimensional maximum entropy generation analytical model for dissimilar friction welding is constructed, which reveals the distribution of the temperature during severe plastic deformation. The effect of metal extrusion along the flash is further introduced to extend the model to a steady-state two-dimensional model, and a steady-state two-dimensional maximum entropy generation analytical model is established by combining it with the constitutive equation of metal plastic flow. Finally, on the basis of the dissimilar interface welding criterion, a steady-state thermal collocation analytical model of dissimilar rotary friction welding (RFW) is constructed. The model does not need to preset the response parameters and can effectively predict the welding temperature, axial shortening rate and viscoplastic zone width after the experimental verification of the RFW of dissimilar collocation. The trend of the calculations is similar to that of the experiments, and the relative errors are within 10%, which indicates good accuracy and reliability.