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When my auto tranny GT is cold, it will run a little "rough" for the first
10 minutes or so with very light throttle, and will tend to "jerk" slightly. Like if I hold it in 1st or 2nd gear (around 1200 rpm or so), just barely pressing the throttle with very little load on the engine, I get a little "jerking" effect... but if I then step into the pedal a bit, it runs fine. When the car is warm this does not happen. I will note that several other newer cars I have driven, including a Chevy and Honda, have acted the exact same way when cold. They will jerk slightly when cold with very little load on them. I would tend to consider this normal. Perhaps they are adjusted to run a bit lean in this condition (cold and hardly any load) causing a tiny bit of surging.
Side note: the reason I experience this is because I always "warm-up" my engine in this manner - I start it up, then almost immediately start driving, but run in 1st or 2nd gear at between 1200 - 1500 rpm for maybe 5 minutes with just a light load on the engine until I see the temperature gauge just start to move (stay on the side streets). This is a much better warming technique than starting a cold car and letting it sit and idle for 5 or 10 minutes like I see a lot of people do. While it may or may not make a huge difference in the long run, I am a firm believer in getting the engine up to or at least near operating temperature before putting a heavy load on it (like having to accelerate hard from zero to 70 entering a freeway, etc). I've seen some guys start a cold engine on a 20 degree day, and then go tearing off at full throttle... not sure how bad this is for the engine, but it can't be good. Oil is still thick, internal clearances are not correct, etc.