2001 ZTEC problem

I have a 2001 SE Wagon with the 2.0 ZETEC engine. When the engine is cold it runs very rough at idle. This can be either sitting still or if I let up off
the gas going down a hill or around a curve. Here is the strange part... If I drive it 5 or 6 miles and turn it off for a little while and start it back up it runs a perfectly however if I drive straight home from work, about 10 miles, it runs rough at idle all the way home. I've tried new plugs, air filter, cleaned the PCV valve, and even checked to make sure the timing belt was ok even though I knew that was highly unlikely. The engine has 112k miles on it. Any ideas??
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Take it do a dealer. That's really odd. What brand of gas do you put in it? If you're using gas w/ no additives that could be an issue.
Lots of people put in the habib gas to save a few cents a gallon not realizing the long term damage they are doing.

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