Chris, I am currently trying to work through the same problem on a 1989 300CE, US version (103.983 motor) . In fact, it's in a 2nd shop for further diagnosis as I write this.
There's an MB bulletin on hot start problems for the 124. It lists several items as possibilities for 'customer complaints of hot start difficulty,' including fuel pressure leakdown (possibly the injectors as Michael mentioned, but also possible: fuel pressure accumulator, fuel pump check valves, cold start valve, injectors, and fuel pressure regulator), zero position of the mass air flow sensor in the fuel distributor, and the coolant temperature sensor (not the gauge, but the input to the EFI module).
I gambled and tried, but failed, to solve this using just the parts replacement theory. New OVP relay, fuel pump relay, fuel accumulator and fuel pump check valves were installed to no avail. (The EHA was replaced a year ago for other reasons.)
If you have the MB 124 manual on CD, it goes into detail on all of this.
A fuel pressure leakdown test isolating the leaky segment of the fuel system might be your best bet, assuming it is a fuel problem.
Hopefully, I will know later in the week the cause of my hot start problems. I'll put this on my original post, which was a few weeks ago here.