Runs great until it heats up, then rough idle and shuts off

I have replaced air filter, plugs, plug wires, distributor cap and rotor. And changed the oil. I am thinking it maybe a throttle sensor or oxygen sensor. It will start up and idle perfectly. Even a little while after it heats up. When I start to accelerate after heated up it will start running rougher and rougher until it shuts off. Then will not restart until it cools down. Then, it will restart and run perfectly until it heats ups and I accelerate, then the same thing. The problem starts when it is hot and I accelerate. Any suggestions?

Oh, and my EGR light is on.