my 1993 300E 2.8 liter is hard to start when temperatures reach 90+, which is commonplace here in the southwest U.S.
i have to floorboard the pedal when cranking it over, then have pump the peddle to keep it from dieing until it clears in about 30-45 seconds. after it clears out, i can drop it in gear and go. i have always used 91+ octane fuel
It sounds like the coolant sensor could be giving an improper signal to the computer.
You can have an automotive professional check it with a scanner and he would be able to see the signal to see if it is correct. He would also be able to see if the engine is running too rich or too lean making it hard to start.
This problem may or may not set a trouble code.
Checking the fuel pressure should also be checked if you have trouble starting the engine. If you don't have the 2 second prime from the fuel pump it will also make it hard to start.
Check out these suggestions and let us know how you make out. If these don't work then we can go on from there.
Try to give as much detailed information as you can so I can help you better.
Just try to do diagnostics of the car, it's easy. The problem can be very different from that you think, sometimes is impossible to find the problem. I think will be something small, but must do a diagnostics first. Good luck you have great car!