After I have been driving for long periods of time or in a lot of stop and go traffic on a hot day, if I turn the car off, it will start, but it will not idle at startup unless I give it gas. If I let the engine cool for 15-20 minutes, it will startup and idle just fine. And if I never turn the engine off, even after driving for long periods, it will idle without dying. I have had multiple mechanics try and find a solution, with no luck, partially because it is difficult to recreate. But I have had the Mass Air Flow Sensor, upper/lower radiator hose, thermostat and gasket all replaced. I have also had the Idle Air Control Valve checked, which was fine. Any other suggestions would be greatly appreciated! Thanks!
I would have guessed a weak fuel pump or the fuel getting overheated somewhere.
Check the fuel pump pressure and follow the fuel line to make sure it is not too close to some hot part.