It is still possible that the CPU overheats, and this can happen when all users log on as that will put it under a heavy load. I'd open the server and clean out all dust, and if possible remove the CPU heatsink, clean it's and the CPU's surface very thoroughly, then apply very little thermal transfer paste and firmly reattach the heatsink.
You can run sfc /scannow while the server is in production, but if this repairs anything it might require a restart, as will the servicepack and windows updates, but you can do those reboots when you want to.