Buick Regal quits

1988 Buick Regal (only 59K) running fine til one day after idling in driveway for 5 or 6 minutes, I drove up the street and the car died a few blocks away. Tried to re-start; it turned over but would not run. Left it for 4 hours, came back; it started right up. Drove 3 miles and it died again. After 3 tries, it finally re-started and I was able to get ita mile home. Left it overnight, came back in the AM and started it right up. Drove 4 or 5 miles and it dies again. Would not start so I left it and came back the next day. Started, drove a few blocks, dies again. Hooked up a tester onto one of the spark plugs and find that there is spark and it fires even while engine dies. The fact that the car does run for a few minutes when cold makes me think the fuel pump is pumping. Thought engine might be over heating so I took out the thermostat. Same results. Can this be some sort of malfunctioning sensor that shuts the engine down when it warms up? Any other thoughts or advice?
Thanks. JK