At least I think it's an air supply question... Our 2000 E320 has a warm starting issue. It starts fine when cold, and fine when hot. However, there is a range in the cooling down process that it just cranks.
I have run tests with two different gas caps, even without the cap, and find that after shut down at normal driving temp (80) it will restart fine until 1 1/2 hours have passed. Then it refuses to catch until another 15 minutes goes by. Then it starts fine.
The local mechanic tried the ring-gear lube trick to no avail. We are kind of surprised that the issue has not "thrown a code", but imagine there are odd intermittent malfunctions that the computer doesn't identify as serious.
I visualize a sticking butterfly valve (or weak spring) on top of the carburetor. Except there isn't one.
Any ideas?