Yes you should look for a better cooler, I have the Intel 13500 in one of my systems and initially used the stock cooler which throttled the cpu in most applications. I had an old Scythe Mugen 5 and just ordered a LGA1700 mounting kit for it and it works very well. This is quite a beefy cooler and the cpu still hits about 80° in Cinebench.
So if you already have an older cooler your cheapest option is just seeing if they offer a LGA1700 kit for it.
Other than that it all depends on what you are willing to spend but a good starting point would be something like the Thermalright Assasin X120 Refined SE which can be found for as little as £15 here in the UK, not sure about pricing in your region. Personally I'd spend the extra on a Thermalright Peerless Assassin 120 SE for around £30.
Yes you should look for a better cooler, I have the Intel 13500 in one of my systems and initially used the stock cooler which throttled the cpu in most applications. I had an old Scythe Mugen 5 and just ordered a LGA1700 mounting kit for it and it works very well. This is quite a beefy cooler and the cpu still hits about 80° in Cinebench.
So if you already have an older cooler your cheapest option is just seeing if they offer a LGA1700 kit for it.
Other than that it all depends on what you are willing to spend but a good starting point would be something like the Thermalright Assasin X120 Refined SE which can be found for as little as £15 here in the UK, not sure about pricing in your region. Personally I'd spend the extra on a Thermalright Peerless Assassin 120 SE for around £30.
*no I don't work for thermalright :)