A6 2.5 TDI: Won't Start When Warm?

I'm having a pretty serious problem with my A6, 2.5 TDI (manufactured in December 1995, 140 hp, 5-cylinder engine)!
'If the car has been sitting for a night, I have to pre-glow it two or three times, and then it starts perfectly. However, if the engine is warm and the car has been sitting for an hour or two, I have to try 10-20 times before it starts. Once it does start, there's a white cloud of smoke coming from the exhaust! WHAT COULD IT BE??? I just bought this car. Since there was no service history, I had a complete inspection done. This means that everything that could wear out has been replaced (timing belt, glow plugs, fuel and air filters, glow plug controller, etc.). I also had the diesel pump checked, but it's fine too! The fuel injection timing was also checked a third time. Audi measured the error codes, but nothing was displayed or found. No one in my area can help me, even if they are very skilled! I would appreciate it if someone could give me a tip. Thanks in advance!!!'

Hi, I would like to have the start-up process checked again, for the fourth time, but this time somewhere else, or by myself, following the troubleshooting instructions in the technical article.

Hi, try disconnecting the coolant temperature sensor before attempting to start the engine 10-20 times. Does the engine start then?

Let's test the battery capacity.

Hello!
'You're not alone with this problem! I have the same symptoms with my C4 from 1995. However, mine starts perfectly fine when I disconnect the coolant temperature sensor connector. The Audi workshop replaced the starter motor for me (allegedly due to low starter speed) - after that, everything was fine for about six months. Now, it only starts after a long cranking or when the temperature sensor is disconnected. The resistance value of the temperature sensor seems to be okay, but I'm going to replace it anyway and see what happens.'
With great compassion.

If the problem occurs even when the engine is warm or at least moderately warm, I would rule out the temperature sensor. Disconnecting it only tricks the control unit into thinking it's very cold, causing it to preheat for a long time. However, if the engine is still at room temperature after 2 hours of standstill, it shouldn't need to preheat at all. Mine starts preheating around 0°C.

However, if I adjust the injection timing as described in the technical article, using a multimeter because my engine control unit doesn't work with simple adapters, then the engine starts poorly.
Now the error message clearly indicates a late adjustment issue, but everything is still working.
Unfortunately, I can't determine what values VAG-Com is currently displaying. Maybe I'll go to a VW dealership out of curiosity sometime.
So, it might be worth trying to set the injection timing to "too early."

Yes, what Christian wrote is correct. I didn't mean to say that the coolant temperature sensor is defective, but rather whether the starting behavior is better when the connector is disconnected. Of course, that would be the case if the injection timing is too late.
The simulated cold temperature shifts the start of injection towards an earlier timing.