SCO - have you checked out all the mechanical potentials? (since i do not have VCDS nor know how to use it I do the manual checks first...)
From how I understand your descriptions:
- Runs rough
- Runs fine on idle
- Poor acceleration
- Starts easily
- Escalate when temperature drops
My immediate thought is that your problem occur when you both need more fuel and the temperature is low.
This
could to my opinion be related to dieselfilter, air in fuel system or restriction in fuel system.
I would have checked the following first since it will not show on a VCDS scan.
- Visual check for leaks of all diesel lines including connectors and caps. (remember if ANY sign of diesel leak there will always come air in...)
- Visual check for crushed, bent fuel lines og diesel cooler with dents or damages that could result in reduced fuel flow.
- Change dieselfilter if you are in any doubt wrt condition of filter or passed 20.000miles/30000km
- If your 2005 neither is equipped with a feed pump in the tank, a lot is depending on the tandem pump. I connect a piece of clear tube between Tandempump outlet and the feed line for PDs. Then I set up a GoPro to surveil the piece of clear hose and take a 10min test run. If you do not see any bobbles after 5 min I would say; make the VCDS ready...
- If you can see on the video that the hose get sucked flat'ish I would recommend to check further the Tandempump and fuel system. That is an indication of insuffisient flow.
Over here it happens on A2s and others with diesel-coolers underneath the car that they get knocked flat by ice-blocks during wintertime and during off-road driving. If no major leak, the symptoms are as you describe.
Dieselfilter life depends first of all on what you shall filter... it is enough to fill one tank from a "polluted" petrol station and even a brand new filter is clogged.... then the Tandempump will have to work hard and will suffer to feed the PDs and then you get rough running engine.
Hope this can be to some help. My apologies for terminology mistakes and strange grammar/spelling... I still suffer from brilliant sea view from the classroom I was supposed to learn English language in
(many thanks to google translate)