Is it a diesel? If so, then your diesel particulate filter (DPF) will be trying to regenerate and clear itself out. The engine fans run at full speed while the DPF is going through the regeneration process, and if you turn the engine off while this is happening, the fans will continue to run for 10-15 mins. You can usually smell something and feel extra heat coming off the exhaust too.
Unfortunately there is no sign that the car is going through this procedure (eg no lights or warnings on the dash). You can use an app called VAGDPF which you might be able to use with your OBD11 module to check how full your DPF is and so you know when its full to take the car for a 30min drive to let the DPF do its full regeneration process.
Have a read of this to give you info, paying attention to the Active Regeneration section as this is the one that will apply to 95% of situations: The diesel particulate filter explained | AutoGuru
VAG DPF app on Android to monitor DPF
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