1987 Honda CRX sputtering and dying

I have a 1987 Honda CRX Si it has a Fuel Injected 1.5 liter with 203,000 miles was rebuilt around 125,000. It has always ran great until recently. As I drive to work in the morning the car begins to sputter as the car starts getting warm. It seems to be temperature related because it does it at the same temp everytime. After it sputters I will come to a stop and it idles fine the second I touch the gas peddle it dies. It will start back up after a couple of minutes. I've replaced the plugs, wires, rotor and cap. A mechanic just replaced the Distributor and said no codes came up on it. The distributor helped with cold start up but it still sputters and dies. Like I said it seems temp related it sputters and dies at the midpoint of cold and normal operating temp.