Your CPU won't die, it'll just throttle hard until it hits its critical temperature then trigger a thermal shutdown. First I'd plug the CPU fan into a different fan header in case the problem is there. You'll get a CPU Fan Warning on boot, but you can disable that if it is indeed the header. If it still occurs, then I'd just get an aftermarket cooler, since by the time you pay for return shipping it'll be about the same amount of money.
