I have been having this problem for about three weeks, becoming progressively worse each time. The problem is almost certainly in the starter or battery.

1.) It could be a short in your starter. It's basically saying "leave me alone and let me die in peace" when you have hot-start problems. (Heat breaks down the insulation.) However, I would expect this after the *engine* got very hot, not the warm outside air.

2.) Your battery is weak, and is not being properly charged by the alternator. Check the Voltage Regulator brushes which you can unscrew very easily from the back of your alternator. This solved my problem entirely. (See post titled, "My 260E is Running Great") The brushes should be evenly worn, and about an inch long (when new). If they are about half that, replace them. (About $30 for parts.)

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2008 E350 4matic / Black/Anthracite

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Gone but not Forgotten:
2001 E430 4matic, 206,xxx miles, Black/Charcoal
1995 E320, 252,xxx miles, Black/Grey
1989 260E, 223,00 miles, Black/Black