Upgrading PC due to cooling issue

Hello all, I currently have a PC I built in 2022. I got a Ryzen 7 3700X and an RTX 3060 for relatively cheap at the time. Recently, I’ve noticed that my game performance drops heavily after an hour or so of gaming. After some troubleshooting, I’ve realized that the CPU is reaching 95-100 degrees Celsius with the stock cooler.

I have plans to upgrade this ASAP, but should I consider replacing the 3700X with a 5800X3D at the same time?

I don’t know if there is a significant impact to performance. I currently play Stellaris and BG3 the most as well as Ghost of Tsushima. My rotations tend to involve RTS type games. Does it make sense for me to upgrade the CPU alongside the cooling? I’ve only really noticed issues on Stellaris (outside of the choppy frame rates from thermal issues).

Thanks