COLD engine problems

[Shumadin]

Here is the thing.
Diesel engine A8/D2.
COLD ENGINE - on start, it hesitates to start, the colder environment the more it hesitates - but after a bit prolonged cranking (2-3 secs) the engine starts to run.
At idle the engine runs ok, it holds rev needle pretty steady.
As I step on gas pedal, and slowly increase rpms, at about 1200-1300 it starts to jerk intermittently. (at that moment, instead of RPMs and other data I get an ERROR message in group 004 in VCDS; BUT I can still see RPMs in the dashboard)
I continue to increase rpms, and at 1500-1800 jerking starts to be very rough, engine stalling.
At 1900-2000 rpms the engine begins to rapidly increase rpms, not so controllable by the gas pedal.
All this happens until the coolant temperature reaches 168-9F(75-6C). After that point the engine runs pretty fine although the gas mileage is bad and car is feeling sluggish at low rpms.
Does anyone know what might be the culprit here?

 

[Garrett 69]

Sounds like it's linked to the cold start system, possibly your pre-heat isn't working. My A3 has a similar but not quite severe issue in the cold, it's solved by a couple of gentle blips on the throttle.

 

[Shumadin]

Sounds like it's linked to the cold start system, possibly your pre-heat isn't working. My A3 has a similar but not quite severe issue in the cold, it's solved by a couple of gentle blips on the throttle.

I'm not sure what goes into that system and how it heats the fuel. Blips don't help. There is one more interesting thing. When I first start it (cold engine) it runs fine for about 1-2 min and then it starts jerking at 1200-1800 rpm. The smoke appears to be white/gray while intensely shuddering. But there is no smoke at idle and the engine runs fine.