Do a voltage drop test on the starting/charging circuits. It's a very common hard hot start issue.
what year is the injection pump? if it's from an 86 or later engine and it has the fast idle that works off the cold start linkage you could have low residual pump pressure. if someone adjusted the idle speed with the throttle stop set screw instead of the right one on the linkage it would make it do that. of course, if you have the original pickup injection pump ignore this post :-)
Yeah only thing I can say is the obvious; I've got an 86 f250 that had leaky return lines that caused just that. Poor hot starting
leaky pump seals, cracked return lines, anything really, can cause the pump to get air, and not start well when warm.
my return line had a crack in it, and it wasnt big enough to leak fuel out, but it was big enough to leak air back in once you shut it off..