A console that sounds like a jet engine and then shuts itself off mid game is usually telling you the truth: it is hot, it knows it, and the shutdown is the protection working, not the fault.
Start with placement because it is free. A console in a closed cabinet, on carpet, or against a wall is recycling its own exhaust. Give it open air on all sides and see if the noise changes this week. If placement fixes it, that was the whole repair.
Then dust. Consoles pull a surprising amount of lint through the intake, and the heatsink fins pack solid over a few years. Compressed air from the outside pushes dust deeper; the honest clean opens the shell and blows the fins out from the inside, with the fan held so it does not overspin.
Then thermals. Dried thermal paste and hardened thermal pads are the classic "it ran quiet for four years and now it screams" shape. Replacing both is a real repair with real improvement, and it is the step people skip because the console still turns on.
Shutdowns that continue after all three point at the power supply or a failing fan, which is meter-and-parts territory.
Which console, and did the noise change with better airflow? That answer helps the next person decide how far to go.