A quick guess...OVP...if the current one is original!

Could also be a fuel pressure regulator.

Do a search on "hot starts"

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car