I have a 2004 a4 1.8t. I have been having this problem continuously for a year and a half. When my car runs and gets warm after about 45 mins of driving it begins to hesitate though every gear with rpm rising until it finally catches gear. I can never get over 65mph. After this accurse for about 15 mins the car will shut off completely. I let it sit for a bit and then turn the engine over and try to drive it. It runs rough and bucks on me and then shuts off again. (no check engine light ever comes on through out this whole ordeal) It will occasionally run for a little before it shuts off on me again never getting over 45mph and bucking through every gear. When the car is not run for a long period of time I have no troubles and it drives perfect. After all this accurs if I let the car sit and cool down it runs like nothing ever happen. I have been through 2 transmissions, cam shaft work, e.c.t sensor replaced, auxilary fan control module replaced, thermostat replaced, engine coils replaced, new spark plugs and still with no success. I'm running out of patience, ideas and money. Please help .......

 

Just throwing ideas out that you haven't addressed, but it sounds like your spark plugs are fine. Maybe the fuel system is not running like it should? Maybe a clogged fuel filter or a few bad injectors? Maybe a knock or cam position sensor, or another engine related sensor?

It would help to have a code reader that displays live engine data. That would help narrow down the list of possibilities.