Car runs about 1 min backfires once and dies

I am working on a 1991 Acura Integra with about 210,000 miles on it. Originally the car was overheating after about 5 miles of driving so I replaced the thermostat and also flushed the cooling. After that the car while idling would be as about 1000 rpm and rev to 2000 rpm then back to 1000 over and over until it would die after about 1-2 min, and I could start it and it would do the same thing but sometimes the interval would change like 600 to 1200 rpm. I changed the coolant temperature sensor and now the car will start and idle for about a min at around 1500 rpm and then with a small backfire die. If I increase the rpms it does the same thing but the backfire is louder. At 4000 rpm it is a pretty loud backfire. About 20% of the time the car dies with no backfire. If I try to drive it dies in the same time interval in the same way. Does anyone have any ideas on where to go from here? Thanks.

Oh, some extra info is I cannot use an inline spark plug tester because of the way the spark plug wire is designed. Also it is supposed to be 1000-2000 rpms idling until the coolant warms up.

Just as soon as it dies, can you restart it and have it run for the same amount of time again?
Have you checked the fuel pressure?

Also check timing. Use a timing light for this, don’t just guess.

If the fuel isn’t being burned completely because the timing is too retarded then it could get into the exhaust system and blow up, hence the backfire.

My thoughts too…timing is probably off.

With that many miles on the vehicle, you might want to check for a restricted catalytic converter. A plugged cat could cause all the symtoms you describe.

Tester

The backfires do indicate timing. The car is old and a timing belt or chain is just general maintenance at this point. If the car is no longer overheating, replace the timing belt or chain. While your at it replace the water pump as well.

Thanks everyone! It looks like a pretty common consensus on the timing belt so I will look into that. Thanks again!