Fiero having troubles staying running

I have 88 fiero se with the 2.5L "duke" and its a 5speed. I payed 200 bucks for it and the only issue is it will run for 15 mins fine and then shut down. i was told it was the ignition module and i tested it about 20 times and it tested fine. So i replaced both of the coil packs (that was the next option i was told). the issue is still happening and i just need some tips.

What do you mean by shut down? Cranks but won't start for a period of time? Then if wait for a period of time, then it will start and do the same thing?

People can tell you this and tell you that, and you can replace parts until the cows come home.....

Time to do a little diagnosis.....

If it cranks but doesn't start, first thing to do is look at TBI.....does the injector spray fuel? If it doesn't, have someone crank the vehicle while you spray carb cleaner into the throttle body....if it starts and runs, you either have a fuel delivery problem.....either bad fuel pump, bad ignition control module, injector, ECM, etc.

If no fuel comes out of the injector while cranking, and spraying carb cleaner into the throttle body has no effect, then you need to check for spark...THIS HAS TO BE DONE ONLY WHEN THE VEHICLE DOES NOT START...use a spark tester at the end of each of the ignition wires, one at a time....crank and check for spark.....since you have two new coils, we know there is not a coil problem.........if one of the coils does not fire, then it's a bad ignition module.....if BOTH of the coils do not fire, then it could be a bad ignition module OR bad crank sensor OR both....

I have run into this problem before.....the problem is the connection between the crank sensor and the ignition module....since the crank sensor is piggy-backed on the bottom of the ignition module, and not knowing how old either is, I would replace both.....

Fiero was a unique looking kind of vehicle....not the greatest ride....in salt areas, it was known to rust out bad underneath.....just making you aware......also look at the wiring harness on the backsiode of the engine to see if it's covered with silver covered tape....that was part of a major campaign for this engine.....

What do you mean by shut down? Cranks but won't start for a period of time? Then if wait for a period of time, then it will start and do the same thing?

People can tell you this and tell you that, and you can replace parts until the cows come home.....

Time to do a little diagnosis.....

If it cranks but doesn't start, first thing to do is look at TBI.....does the injector spray fuel? If it doesn't, have someone crank the vehicle while you spray carb cleaner into the throttle body....if it starts and runs, you either have a fuel delivery problem.....either bad fuel pump, bad ignition control module, injector, ECM, etc.

If no fuel comes out of the injector while cranking, and spraying carb cleaner into the throttle body has no effect, then you need to check for spark...THIS HAS TO BE DONE ONLY WHEN THE VEHICLE DOES NOT START...use a spark tester at the end of each of the ignition wires, one at a time....crank and check for spark.....since you have two new coils, we know there is not a coil problem.........if one of the coils does not fire, then it's a bad ignition module.....if BOTH of the coils do not fire, then it could be a bad ignition module OR bad crank sensor OR both....

I have run into this problem before.....the problem is the connection between the crank sensor and the ignition module....since the crank sensor is piggy-backed on the bottom of the ignition module, and not knowing how old either is, I would replace both.....

Fiero was a unique looking kind of vehicle....not the greatest ride....in salt areas, it was known to rust out bad underneath.....just making you aware......also look at the wiring harness on the backsiode of the engine to see if it's covered with silver covered tape....that was part of a major campaign for this engine.....
What i mean by "shutdown" is that you can drive the car, and it ride and run excellent, but once the engine reaches about 175 degrees its like you just turned the ignition off, all lights stay on but the engine just stops. Fuel comes out of the injectors whenever it is turned over, i have not had time to check the spark but as soon as i get the chance. I am 17, and on a tight budget funded by myself because my parents didnt want me to get the car and said they would have nothing to do with it, so im trying to figure out what is wrong and fix it in the most cost effective way. But thanks for the tips and i will definetly check them out and let you know what i discovered.

Also, yes whenever it shuts down if you wait about 30-45 mins then it will start just fine. thanks again