Rough idle on 2001 Mazda Tribute

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When starting the car after it has set for several hours, the engine coughs, sputters and tries to die. After driving for 5-10 minutes, it runs fine.
(1) Answer
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Cold engine coughing and sputtering...leads me to think that there may be problem with the idle air control valve sticking, causing air/fuel mixture issues. Something in that area. Also check for any vacuum leaks or unmetered air (broken air tube/air box) getting into the intake.
I had similar issues coughing/sputtering-thereatens to die, Idle air control valve was replaced-still the same issues are present. What else besides maybe a vacuum leak (which I did have one, but we fixed it too). looking for a "what next to look for" thanks.
Thinking of it today, my thoughts of coughing and sputtering and almost stalling makes me think of an unmetered air leak - broken air box, air tube leak. Or, an issue in the EGR system can do it. Last, fuel pressure is of course a possible cause - check base fuel pressure and then bleed down. The final thought would be about fuel quality -- and fuel blends. A warm weather blend in cold weather can cause poor running, and likewise cold weather blend in warm weather can cause rough running on a "hot soak" - this is when the car is driven, shut off for about 10 minutes, and then restarted.
In any case, you can do some basic diagnostic testing with a good diagnostic tool to check some of this out.
I had the exact same problem and it is solved by replacing the upper and lower manifold gaskets. Idle control valve replaced with zero result -- not the problem. EGR also replaced with no result. I sincerely hope that helps!