That sounds like a failing fuel pump relay, good until it overheats or fails, then ok after it cools. A bad fuel pump will do the same thing but check the relay first, it is the easier and cheaper option to go to first
Check your fuel filter and pressure.
why is my 1995 buick roadmaster running hot
Fuel pump is gping out it may have enough fuel to start then it works like a vacuum but the pressure is not enough to keep it going. Same thing happend to my Buick Lasabre.
There are several reasons that can cause your 1995 Buick Century to quit running. The most common reason is a lack of fuel. A bad fuel pump can cause the engine to quit running.
It's probably the fuel pressure regulator.
If no light illuminated first step check fuel pressure
why is buick lasebre running hot
It sounds like the Throttle Position Sensor needs replaced.
Especially if you are in cold areas, it takes more pressure to circulate cold oil. When it warms up, the oil flows easier through the system reducing pressure.
Bugatti Buick
There is no ideal pressure. Of course the oil pressure will be higher when the engine is cold. After it is running and at full operating temp, the pressure should read at least 10 lbs while idling. The pressure will be directly related to how many miles are on the engine and the amount of wear. A new engine will have around 40 lbs when hot and running at 2,000 rpms, and around 30 lbs at idle.
Buick Blazer