I have experienced the same thing. It happened to me only a few times since I've owned the car. No indication that the car is hot but the fan keeps running for a long time after turning the car off. Very weird!
This is perfectly normal, it us related to DPF regeneration.
Every 500 miles or so, your car forces a DPF (diesel particular filter) clean. It does this by adding an extra pulse of fuel injection post combustion.
This raises the exhaust temperature high enough to burn off the ash collected in the DPF.
Most of the time you don't notice it, although you may see a high idle speed.
If you shut the car off in the middle of a regeneration, or shortly thereafter, the fans will run as the underhood temperature is high. You may also notice a slight burning smell. No worries, everything is fine. Just let it go.
VW TDI forum, Audi, Porsche, and Chevy Cruze Diesel forum
A forum community dedicated to Audi, Volkswagen, Porsche, and all turbo diesel owners and enthusiasts. Come join the discussion about performance, modifications, troubleshooting, TDI, maintenance, and more!