Car shuts off after warming up.

Hi, I have a '98 Hyundai Tiburon. The problem is, that the car cuts off after a certain amount of time. If I start it and let it idle, it'll run for atleast 20 min. If I drive it, and hit the highway next to my house, it'll cut off after about 7 min, which leads me to believe it has something to do with temperature. What happens when u drive it is, you'll feel the engine stutter after 7 min, and after that, if u let the RPM drop below 1,100 the car shuts off. If u keep pressure on the pedal, you're fine. I've had to get it home by keeping the engine reved and throwing it in nuetral at stop signs and traffic lights. When the cars shuts off, you can't restart it. The only way to immediately restart it is to use starter fluid and hold the pedal down, which makes me think it's a problem with fuel delivery. The thing is, if you let the car sit and cool down for an hour or so, it starts right back up, no problem, no starter fluid, which again, makes me think temperature. It's not a bad fuel pump. I've replaced the old one, and even exchanged the new one for another new one, just incase it was defective right out the box. I've also swapped the relays for the fuel pump, but no luck there either. Any help would be greatly appreciated.