Hate to tell you, but it's probably just a bad starter. I had the same problem recently with my 300D--the starter wouldn't work when it was hot, turn the key and get nothing.

Lots of great suggestions here such as tapping the starter with a hammer, verifying ground connection from the battery, and jumping the terminal on the passenger-side fender to bypass any ignition/neutral safety switch problems, but none of those worked and I finally just had the starter replaced. That solved the problem.

Charlie

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05 E320 CDI - 185K miles
82 300D - 200K miles (sold)