I have a 2008 Chevrolet Impala with approximately 150,000 miles and when the engine is shut off there is a loud clicking sound from under the left dash. It will persist for several minutes but will stop on its own. Has been occurring fore several months. Now the heater will not produce heat.
What you might have been hearing is the heater door or the heater core valve trying to close. The door does usually close on some models when turned off so it might be that which would lead into your heater issue. I believe the heater door and the heater core valve on your car are elctronic ally actuated by what is reffered to as an, "Actuator". The can have issues moving, not work all the time or fail compleltely. It sounds like one of the two was having trouble, probably the vent door, moving and the drag on the actuator wore it out and now the heat does not work. There may be one actuator for both the vent door and the haeter core valve itself. The heater core valve is what opens and closes to let hot coolant into the haeter core to produce heat in the car.
More than likely getting the acutator replaced will solve your problem, but I would make sure that smooth movement of the door and the heater core valve were checked because if there is a problem with one of them it will wear out your new actuator.