When I run my Ryzen 5 3600 on the stock cooler (the one that came in the box) at hig loads (prime95 AVX On) I reached 92~93°C, but it never shutdown the system.
I would really check what herrwizo wrote, but I would start by making sure the stock cooler is properly sitted on the CPU and that on the Asrcok b450 pro4 BIOS the overtemperature protection option is set to atleast 90°.
Also theres no need for watercooler (of course feel free to do it if you can afford it) unless you live in a very extreme hot pace with high temps all year. I fixed my temps issues with a cheap DeepCool Gammaxx GTE, but even the inexpensive Gammaxx 400 will be an upgrade over the stock cooler. Keep in min that a 120mm radiator aio water cooler wont be better than an aftermarket tower cooler, so get atleast one with a 240mm radiator.