This winter I have noticed that the radiator fans will come on when the car is shut off, sometimes only for a second, sometimes for up to 20 seconds. My car is a 2007 3.0.

Today I needed to move the car off the driveway to get into the garage, outside temperature was -15C and the car had been sitting outside all night, so it was thoroughly cold. Started the car, backed it to on to the street, shut it off, and the radiator fan came on. There should have been no need for the fan to come on, as the car ran for a minute maximum and would have no heat in it. I have had it come on in similar situations where it was cold outside and I shut the car off before the needle on the dash gauge has started to move and the fans will come on.

I thought if it was a fan module then the fans tend to come on and stay on, rather than only coming on when the car is shut off. The dash gauge seems to behave as normal and the coolant is full.

 

Your fan is working correctly. When you start it up the thermostat is closed and water around the cylinders heat up quickly. Since they are near the temp sensor the ecu is seeing high heat from the cylinders and is signalling the fan to run. The high temp fades quickly and the fan shuts down. Lucky you your fan control module is in good shape.

 

Starting from -15C/ 5F and running for less than 1 min there isn't enough heat in the coolant to do much of anything. The hoses/ overflow bottle and block were still (very) cold to the touch. This is a fairly new thing, it didn't do this last winter, so that makes me think something is going on.

 

Faulty fan modules are a well known fault on the X Type, mine used to do this as well until I changed the module. I bought a used one off Ebay. There are two types, for early and late cars so make sure you get the correct one if this is the fault.