Think of it this way. Any decent modern CPU can dissipate anywhere from 65 to 125 (or more) watts, depending what it's specs are and how hard you are pushing it. Now you know how hot a 60 watt light bulb gets.
Basic premise: the cooler your electronics run, the longer they will last. Also they electronics tend to slow down when they heat up. For running word processors, spread sheets and stuff like that, a standard heat sink with fan will do the job. If you are gaming with an AMD 8 core processor, you want to have some serious cooling, liquid I mean.
If you meant to ask if it can run without a heat sink, no, it will burn up before you finish booting up your computer.
And make sure you keep you air cooled heat sinks clean and free of dust. I have replaced more than a few CPU's on laptops where people have had a build up of dust and lint which completely blocked air flow thru the fins. And don't forget the heat transfer paste. They don't last long without that either.