A cooling system (500) for an electric drive system includes a cooling duct (502) extending between a first component and a second component. A motor (336) driven fan (510) creates an airflow within the duct. A first temperature sensor measures a first temperature of the first component and a second temperature sensor measures a second temperature of the second component. An electronic controller (540) receives the first temperature and calculates a first temperature difference between the first temperature and the first temperature limit (802) to generate a first command (836) for the motor (336). A second temperature difference between the second temperature and the second temperature limit (802) generates a second command (836) for the motor (336). The controller (540) then selects the greater of the first command (836) and the second command (836) to yield the maximum command (836), and controls the motor (336) based on the maximum command (836).