I have a 3rd generation i3 that runs at ~60 degrees Celsius on full load with it's stock cooler install. Should I upgrade to a cheap, aftermarket cooler like the Cooler Master Hyper TX3 or 212, or will there be little to no difference in terms of the performance and longevity of the processor?
As long as your only hitting low 60's under Load your OK.
IB does not throttle down until around 95 C!!.
That said, I'm a firm believer in the cooler the better, and the Intel HSF is at the BOTTOM of the totom pole when it comes to performance. personally even though your temps are OK, I'd invest in a 3rd party HSF - the Most recommended seems to be the 212 EVO.
Personally I do not even take the Intel HSF out of the Box, I leave it in the box to weight it down - LOL. This is even if I do Not intend to OC (my wifes system).
Do have to keep the HSF if by remote chance you have to RMA the CPU.