[aerohead]

You might want t look at an 'escapement' mechanism, as used in mechanical clocks.
* Your air 'door' could be subjected to constant, door-opening, 'return-spring' tension, tending to keep the door open.( fail-safe )
* When the radiator temp sensor triggers voltage to the cooling fan, voltage would also be enabled to an escapement dog solenoid, releasing the dog from it's normally- extended position, allowing the return spring to pull the door wide open.
* The 'dog' releases the escapement gear, the return-spring pulls the door open, while the cooling fan operates.
* When cooling is satisfied, and the radiator thermal switch goes open-circuit, killing the cooling fan, the solenoid which engaged the dog to the gear would go 'dead' and the spring-loaded solenoid would extend the dog, capturing every tooth of the gear while the motor ratchets the door back closed.
* The door motor does not have to run 'forwards' and 'reverse.' Only 'forwards.'
* 'Opening' is just a passive function, because of the return spring.