Which processor is this?

For the modern systems a processor will run at throttled speed when overheats before going into overheat shutdown.

Throttled speed means sub-normal speed, meaning running at lower performance.

Devices like processor are made to run at high heat so even if you run 24/7 high heat it will still be fine, life span may shorten but it still runs fine. It won't shorten until it KO within next 3 days.

What's your motherboard?

No point changing cooler if your board can't overclock or you don't intend to overclock.