White smoke at medium engine temperature (in a German-made car)

Audi A4 Avant, first registration 2007, engine from Germany, mileage 170,000 km.

Good evening everyone, I've been trying to use the search function lately, but I haven't quite been able to find a solution to my problem yet, so I'm going to bother you with it.

When I start the car, it runs smoothly at idle. A little more torque when starting would be nice, but it's okay.
As soon as the machine has been running for 2 minutes in these ambient temperatures, the idle is unstable. The exhaust fumes smell extremely chemical, and after a short time, white smoke also starts coming out of the exhaust pipe.
Well, the surprise is that once the engine reaches operating temperature, everything is fine, as if nothing had happened.
No noticeable oil or coolant consumption, the error memory is empty, extended highway drives have been performed, and I believe the fuel consumption of 6.25 liters per 100 km is also acceptable.

The previous owner unfortunately failed to disclose this defect to me, but when I inquired about it, he confirmed that the problem had always existed. A power distribution (PD) element was replaced by him at the beginning of the year, but there is no documentation to prove it.

Okay, here are my ideas:
MWB13: Check idle speed control.
If there are discrepancies between the PD values, swap them and see if the error follows.

View the sensor data blocks from the DPF, including the last regeneration cycle, load level, etc.

Do you have any other ideas?

Best regards.