The only way to be sure is to monitor temps. I'm guessing this is a pre -built system. If it came with an app to monitor the case and CPU temps, use it. If not, try to identify the mobo or chipset - you might be able to get monitoring software from the manufacturer. Otherwise, try downloading a freeware app like Motherboard Monitor.
If you can't overclock and keep the temp down to a reasonable level, then upgrade the HSF. Swapping the HS should be done with care, and only if you truly need something different.