If it happens only when it is hot outside, and never at night, then I would blame the crank sensor.

I had the exact same problem a few years ago.

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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