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Heat soak related engine stalling is a common symptom of CPS failure, later after it cools it will start right up. Please also check to ensure that the connector is not loose and firmly seated against the sensor. Without a CPS signal the vehicle will not start, it is a required function the ecu must see.
I believe the e420 is close enough of a model for illustration purposes:
-Auto Tech Guy
Friendly Auto Tech
ASE Certified Technician, Engine rebuilder, Turbo specialist, Engine Diangnosis