Hi Richard, Your Neon has a high pressure fuel system so it cannot vapor lock. If the fuel is cutting off in hot weather I would suspect the fuel pump. It can overheat and shut down. The other thing to check is the fuel pump relay (located in the power distribution box on the left side of the engine compartment). It can also overheat and act up. Check the fuel pressure when the vehicle is acting up. It should be about 48 PSI. If it is too low then check for power to the fuel pump when the vehicle is acting up. It should be at least 12 volts at all times the engine is running. If it is bad, look at the relay. If it is good look at the pump.
If the fuel pressure is good at all times then your problem is somewhere other than the fuel system. Good luck and let me know if you need any more help.