Based on what you described, something with the ignition is getting wet and causing the rough idle when cold. When it gets hot, it dries out and runs better.
Here is a little trick I want you to try. When it is dark, start the engine, open the hood, and mist water on the coils, wires, plugs. On the entire ignition system. Then in the dark, if there is a problem, you will be able to see an arc. Where the arc is located is the problem.
If you're on the east coast (or near), I've seen the news. WOW! I'm near Pittsburgh. We've had rain, but nothing like what you are seeing. My sister is near Lancaster, PA and they are having all types of problems. Good luck with everything and I hope what I said helps.
Joe
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Friday, September 9th, 2011 AT 1:27 AM