Most old procesors are still good, as long as they are dual cores anyway.
And about overheating, yes they do have such issues, but just because a lot of the cases I see them in (including my older case) weren't designed with them in mind. For example it's very common to find them with PSUs a few cm over their fan, with PSU fan blowing hot air onto them.
Swapping the case with a slightly modern one (very slightly), that places the PSU in an entirely different position and adds a case fan is usually enough to "fix" the issue.
The one I'm using atm was one of them as well.