Why does Car start but after the engine gets hot you cant get it to start back up until the engine gets cold again?

what year is the car? it possibly could be that the choke is not disengaging after the car has warmed up. If the car has an automatic choke (powered by an electronic servomotor), that motor may have broke and left the choke on allowing the car to run when cold but not when hot. Other than the choke, your idle speed may be way too low, so check timing and fuel injection/carburetor tuning. If none of that seems to help check the ignition and make sure the plugs look good, sometimes bad plugs don't work if there isn't plenty of fuel.

hope this helps...