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This study proposes a multi-objective finite control set model predictive control (FCS-MPC) for traction motor drive systems in electric/hybrid-electric vehicles. The proposed method seeks to find the most optimal drive with respect to three objectives, i.e., electric power quality, inverter thermal cycling, and motor thermal cycling. Suitable lumped-parameter thermal models are used for the inverter and the motor based on validated methods in the literature to estimate temperatures. The estimated temperatures are integrated into the multi-objective control law to obtain the desired trade-off performances from the drive system. This paper shows that by adding inverter and motor thermal models into the FCS-MPC, thermal cycling can be reduced in the inverter and the motor while maintaining satisfying speed/torque requirements. The proposed methodology is tested via a standard driving schedule for an interior permanent magnet traction motor in a hybrid electric vehicle.