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Battery electric vehicles (BEVs) are currently enjoying rising sales figures. However, BEVs still have problems with customer acceptance, partly due to limited driving ranges. To improve the situation, this paper introduces a novel approach utilising temperature-dependent efficiencies using an economic model predictive control approach (MPC) in combination with an active grille shutter in order to accelerate the heating of the permanent magnet synchronous machine. The measurements of temperature-dependent component efficiencies on a powertrain test bench are presented and analysed in detail in the speed/torque range. Thermal models based on the lumped parameter thermal network approach were developed and validated as part of the system-level validation against a US06 wind tunnel measurement. After the build-up and implementation of the MPC, various simulations were conducted. For the investigations, three driving cycles were considered at component start temperatures of 20–80 °C. The results show that using the MPC with the grille shutter can save 0.69–2.02% energy at the HV level compared to the rule-based control with a shutter, of which up to 1.02% is due to temperature-dependent efficiencies. Comparing the MPC with the grille shutter to a vehicle without a shutter, savings of 2.8–4.2% were achieved, while up to 1.67% was achieved due to temperature effects in the powertrain.