BMW: Starting, fuel injection system, bmw 325

Question
I have a 1988 German specs BMW 325 in great condition except for hot startig. What I mean is when I first start the car when its cold it works fine.  When I have shut the car down after driving and let sit for 10 to 20 minutes and try to start again it usually starts but after about 4 seconds it starts to run extremely rough until it simply dies.  If I rev it up past 3000 rpms for a few seconds it usually clears up.  Do you have any advice.  

Answer
sounds like the fuel injection system, From the description it sounds like the starter is turning the motor but it is being starved of fuel. Therefore when u rev it your forcing more then the normal ammount of fuel. I would say the problem is either between the Fuel pump, injectors, and or injector pump.

I would have a diagnostics performed by BMW it is more expensive but since there are so many possible points of failure here I would rather pay more and get an expert diagnostics from the dealer then deal with a small shop that is not as qualified to diagnose this type of problem. best wishes.