Check that your heatsink is properly seated and that your computer's internal fans are working. It is possible that the heatsink has unseated itself due to vibration. It is possible that even if they are spinning that they are doing so at a reduced rate. While the computer is off, try giving the fan blades a flick with your finger. If they do not spin freely, they are getting gunked up and may need to be replaced or disassembled and oiled. You may also wish to apply more thermal compound between the CPU and heatsink.
Also, the past few days I've felt like the computer is going slower (but I'm still not entirely convinced that it isn't in my head) in general, could this be related to running too hot?
Yes, overheating computers will downgrade their CPU clock speed in an attempt to avoid a meltdown.
Thoughts? Tips to prevent overheating in the future? I damn near panicked when the computer shut off without any warning and wouldn't turn back on right away... I'd like to avoid repeat episodes. (although it may end my procrastination on back-ups)
Disable variable fan speeds in the BIOS and always operate the fans at MAXIMUM POWER. The fan-speed thing sounds like a good idea in theory until you realize that waiting until the computer is overheating before increasing the cooling is like closing the door after the horses have fled: The fan speed should have been increased BEFORE the computer overheated.