Geez, Bobby, you could grow tomatoes in there! That's BAD. I've seen a few this bad, but not many. It's a good advert for doing it regularly.
Herb, on a dual-core, 55-60 deg is well within limits, and nothing to really worry about. If it gets up to 80 or more, regularly (it will get that hot on occasions when working hard, but should cool down again once the workload is reduced)then definitely there's an issue.
Cooling fans do die too (and a noisy one WILL drive you crazy), but, in a desktop machine, they are cheap and easy to replace yourself. For a laptop, it means a trip to the service-man.
A dead/slow/noisy fan in a desktop PSU (power supply unit, where the cord goes in) WILL kill it, sooner rather than later. Replace the PSU, asap.
Don't oil a noisy fan, it won't help, and may kill it altogether.
My laptop has a two-speed fan, you can hear the fan shift into 'top gear' when the CPU is fairly busy.