Overclocking CPU Heats up while idle / away from computer

My computer's fairly old now, and pretty pathetic for a modern day gaming computer. I've had many issues before, but they were always able to be fixed -- or at the very least understood. One thing I've noticed recently is that my computer tends to heat up far too hot whenever I leave it running idle for about 5 minutes -- even when watching videos (http://I.imgur.com/WsqU0yJ.png Blue is GPU temperature, Green is CPU. It can, and will, get up to 80 degrees) and just goes back down as soon as I reactivate my computer.

The only thing I can think to link it to is my recently running its fans at maximum speed all the time so I don't forget to manually set it through speedfan and accidentally let my computer burst into flames by limiting its fan use to 40% while I play games. I'll admit I don't know *much* about computers in general, so my question is: Would having my computer run this low in temperature (normally 28 in the morning, around 35-50 in evening depending on heat that day, and usage) mess with something? Or is it just about time to reapply some thermal paste, upgrade my computer or simply be more vigilant in setting my fan speeds?

I'm currently running an old AMD Athlon ii quad core processor.