Have you run diagnostics? Use HWMonitor to monitor temps. I'd tend to believe the bios. Check to make sure your HSF hasn't come loose. Remove the dust from the heat sink and case. If this is a new build, be sure you used the correct amount of thermal paste when you installed the heat sink.
Given you are getting a warning about your CPU overheating, that is what you should fix first. Remove the old thermal grease and put on a fresh set. Then it probably wouldn't be a bad idea to run memtest86+ again to see if the memory errors go away or persist. There's nothing saying you couldn't have two separate issues at the same time.