I had a similar issue on my 300SEL. However, before it dies, it would run very rough. Once cooled, it would start again.

I agree with ILUVMILS - However, you can also put an ice pack on the ignition control module if it is hot and has died. If t starts immediately, the control module is the issue. Found a used one with warranty and no more issue!

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2012 Mercedes E350
1988 Mercedes 300SEL
1996 Nissan Pickup
2003 BMW K1200GT