mz500

I have a 2006 Cabriolet w/3.0L, 83000 miles. It runs rough when cold, after a few miles the roughness goes away and car is okay .Could it be tires, they are speed rated W, should be H for this car? But sometimes it's feels so choppy I'm waiting for something to go or fall off. Just had car inspected and suspension checked out fine. If it were a mechanical problem like bad plug or 02 sensor, a warning light would illuminate. Any ideas?

Thanks,