I suffered with same problem for almost 2 years. I could start the car hot only by pouring cool water over the IP and fuel filter. Eventually I did notice a tiny air bubble moving through the fuel line every 10 seconds or so while engine was running normally. Replacing the flexible fuel lines in engine compartment solved the problem. Apparently even a tiny leak is enough to lose prime after 20 minutes. Why it would easily start cold with that condition is beyond me. But I no longer have to think about it, either!