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Friction press joining is an innovative joining process for bonding plastics and metals without additives in an overlap configuration. This paper presents for the first time a model-based approach for designing a multi-variable model predictive control (MPC) for friction press joining. For system modeling, a differential equation based on the heat flows was proposed and modeled as a torque-dependent function. With this model, it is possible to consider cross-effects between the axial force and the friction zone temperature. With this theoretical approach, adaptive model-predictive process control was implemented and validated for different material combinations (EN AW-6082-T6; EN AW-2024-T3; PE-HD; PA6-GF30; PPS-CF). It could be shown that the MPC has excellent control accuracy even when model uncertainties are introduced. Based on these findings, a 1D Finite Differential Method multi-layer model was developed to calculate the temperature in the plastic component, which is not measurable in situ (r = 0.93). These investigations demonstrate the high potential of the multi-variable MPC for plastic-metal direct joining.