The only times I have experienced problems as you have described, the fuel delivery was being adversely affected by a clogged prefilter, and old fuel lines. I presumed the old fuel lines were leaking air into the system when they were hot, and sealed better when they were cold. Never did a post mortem on any of the hoses, but learned to replace them and the little plug on the number four cylinder injector at the first sign of any leakage. It is a two year (approximate) interval. The clogged prefilter was a recent experience, and the only time I have ever seen anything in that filter. I routinely (once a year and, depending on how the car is driven or quality of fuel used, possibly more frequently). The filter event was not a hot start problem, it was one of a series of problems that caused a "never start with the starter" problem, but "always starts by rolling and dropping the clutch in second gear" that I recently overcame and discussed here earlier.

Jim

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Own:
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles

Owned:
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)