Those early 4.5s with the old fuel injection suffered from hot start problems. The fuel vaporizes in the lines (hence the term "vapor lock"). One quick fix is to spray the injection pipework with cool water if you're in a hurry. Additionally, cycling the key on and off a few times will move cooler fuel to the engine, and should assist in starting it. I am fairly certain that you can retrofit a setup from MB which can be mounted on the electrical rack in the engine bay which will automatically run the system in cold start mode at all temps to accomplish the same thing as manually cycling the key on and off. Hope this helps!
Precision Motorcars, Cincinnati, Ohio
'67 250SE Cabriolet
'93 300E 2.8