I'm curious about your problem and interested in learning how to troubleshoot these cars. I'm gonna take a shot in the dark and make up a suggestion; does giving extra gas during a warm startup help/change anything?
Since it starts when cold I assume that you have air, spark and fuel in the combustion chamber.. I don't see how any of this should change when warm, but maybe there's not enough fuel.
Also, you say that the car runs fine when cold. Does that mean that it has the acceleration and rev-response into the high rpms of a healthy engine?
I am also curious to know if the engine even sputters when it turns over when warm (i.e. is there conclusive evidence of a spark in the chamber).