97 Bonneville - Intermitten Failure to Start

If my car is cold it starts fine. If it is warm it starts fine. Its somewhere in between that is the problem. The starter will engage and turn the engine, but it won’t start. Also as the car warms up it will run rough for about 10 to 15 seconds and then go smooth again. This is somewhere between 150F and 200F on the temperature guage. Once it goes over this temp I have about 2 hours of engine-off time to start the car. If it goes longer then the car won’t start for about another hour or so. When the car is started it has no other issues, fuel mileage is fine, accerlation is fine. Recently, after the car is started and warm, I get a whining noise like a turbine engine, which winds down for a moment after the engine is turned off.