Do you mean the starter will not turn the engine over at all when the engine is hot, or do you mean you can crank it with the starter and the car will not start and run?
If it is the first case, the starter acts like it is dead when the car is hot, you may have a worn out starter. Seems a little odd for your car, but it is more common on Diesels as they can frequently be abused, cranking too long and getting the stator windings (electrical coils in the stator) hot enough to damage the insulation on the wires. This damage is more apparent at higher temperatures and so when the engine says it is 80 degrees C, the area near the starter (on a Diesel it is near the exhaust manifold/pipe) can be much hotter. Since starters are used very intermittently, for short periods of time, they cannot be operated at their rated capacity continuously or they will overheat. If they were sized to run continuously they would be huge and heavy, so the solution exercised by automakers is practical and usually gives good starter life.
So, it sounds like you may need a new or remanufactured starter. Be sure you get one rebuilt by Bosch, not a local guy unless you are sure he will test the winding resistance with the stator hot. It is typical for Bosch to rewind Diesel starters when they are remanufactured. Good luck, and I hope this helps, Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)