Audi A3 fan staying on even when key out

Sure it's not just the DPF regenerating ?

If it's the DPF regenerating , you may notice intense heat and a smell of burning , perfectly normal .If not that , could be engine coolant temp sensor .

Fans controlled via the ECU so I'd start with a scan.

I believe there are 2 sensors , it's the engine temperature sensor that normally needs replaced .But you wont need one or have to waste money on a scan if it's just regenerating .