What you described sounds like a bad crankshaft position sensor. When they start to go bad, often times they are affected by heat and fail until things cool down. Take a look through this link and let me know if it mirrors what you are experiencing:
It that seems possible, we have two choices. First, if you have access to a live data scan tool, see if there is an RPM signal when you have a crank no start condition. Or, simply check to see if there is spark to the plugs. If the sensor fails, you will lose ignition spark.
If you find no spark or no RPM signal, replace the sensor. Here is a link that shows in general how it's done:
Here are the directions specific to this vehicle. The attached pics correlate with the directions.
1996 Pontiac Firebird V6-3.8L VIN K
Crankshaft Position Sensor Replacement
Vehicle Powertrain Management Sensors and Switches - Powertrain Management Sensors and Switches - Computers and Control Systems Crankshaft Position Sensor Service and Repair Procedures Crankshaft Position Sensor Replacement
CRANKSHAFT POSITION SENSOR REPLACEMENT
Crankshaft Position Sensor
Crankshaft Position Sensor Shield
REMOVE OR DISCONNECT
1. Be sure ignition switch is in "OFF" or "LOCK" position.
2. Serpentine drive belt.
3. Crankshaft balancer bolt, balancer, and key from crankshaft.
4. Fuel pump/engine oil pressure sensor wire harness retainer clip from shield.
5. Electrical connector from crankshaft position sensor.
6. Crankshaft position sensor shield from front cover.
7. Studs mounting crankshaft position sensor to front cover.
8. Crankshaft position sensor from front cover.
NOTE Sensor 0-ring for wear, cracks or leakage. Replace if necessary.
INSTALL OR CONNECT
1. Lubricate sensor 0-ring with engine oil.
2. Crankshaft position sensor to front cover.
3. Studs and crankshaft position sensor to front cover. Tighten Studs mounting crankshaft position sensor to front cover to 30 Nm (22 ft lb).
4. Crankshaft position sensor shield to front cover.
5. Electrical connector to crankshaft position sensor.
6. Fuel pump/engine oil pressure sensor wire harness retainer clip to shield.
7. Crankshaft balancer key, balancer, and bolt to crankshaft. Tighten crankshaft balancer bolt/screw to 150 Nm (111 ft lb) 4 degrees.
8. Serpentine drive belt.
Let me know if this helps or if you have other questions.
Images (Click to enlarge)
Thursday, July 2nd, 2020 AT 7:17 PM