Fried CPU

[YourFoxyGrandma]

My CPU began overheating for no apparent reason recently. In the time it took me to figure out what was going on, I'm pretty sure some permanent damage has been done as I'm getting blue screens now every once in a while. I'm not sure what to do--my heatsync and fan appear to be working properly and I have extra fans on the front and back of my case for improved airflow. Still, the CPU idles at around 60C.

What should I look into replacing? Just the CPU? Motherboard as well? A new case? Any ideas as to what's going on?