The I9 uses a FCLGA1151 socket while the B560M-A AC M-ATX Motherboard has an LGA1200 socket so if that was the one you ended up getting then you will need to get another MB for the I9.
That part @puzzlezaddict will be better at answering.
@simsical-musical The most important thing here is to get your temperatures under control. The more powerful processor options your motherboard supports produce more heat than the one I believe you currently have, so swapping out the CPU would only exacerbate the problem.
Unless. How comfortable are you with taking off the CPU cooler and examining it? It's possible that the cooler isn't mounted properly, or that the thermal paste wasn't applied properly, or even that the shape of the piece that contacts the processor's heat spreader isn't perfectly flat, which would make it less efficient. All of these are entirely fixable and for a much lower cost than a better CPU.
First though, please let me know what kind of temperatures you're seeing. Download hwinfo from here:
https://www.hwinfo.com/download/
You don't need to install anything if you don't want to; just choose the Portable version, unzip it, and launch it from Downloads or wherever you want. (If you would like to install, be sure to click the button for hwinfo itself and not for lansweeper.) Restart your computer, and don't open any other apps. Launch hwinfo, choose "sensors only," and click the icon that's a sheet of paper with a + sign to start logging. Save the file to your desktop for easy access later.
Wait five minutes, open Origin, launch Sims 4 and play for 20 minutes or until your computer crashes. Click the same button to end logging, or if your computer shut down, the log should be intact to that point. You can upload it to a third-party free filehosting site and link it here. Please leave it in .csv format, or if you use OneDrive to share, please compress it in .zip format instead.
Next, please remove the side panel of your case, the one that gives you access to the hardware, and repeat the test. This will show whether the issue is mostly airflow, which might be fixable with more fans; or more about the CPU cooler not doing its job.
