A system and methods for a vehicle are provided for adjusting each of a speed of a radiator fan and a position of grille shutters of the vehicle responsive to a temperature at a wastegate exceeding a temperature threshold. In one example, a system may include a radiator fan at a front end of a vehicle, an engine coupled to an exhaust passage, a turbine in the exhaust passage having a bypass conduit, a wastegate positioned in the turbine conduit, and the wastegate receiving airflow from downstream of the radiator fan via a cooling duct.