Rough idle on 2001 Mazda Tribute

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.

Asked by for the 2001 Mazda Tribute
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!