The cooler that comes with your cpu will work fine as long as you use your cpu in the way it was meant to be used even if you you your computer for heavy gaming and under heavy load constantly. At worse case if your cpu got too hot, which is unlikely, your cpu would throttle itself to a lower speed and allow the extra heat to be dissipated.
The way it was meant to be used is that you plug it into your motherboard and do not raise the cpu above its manufacturer limits 'ie overclocking'.
Some people who do not overclock still use an aftermarket cpu cooler, i am one of those people. The reason I use the aftermarket cooler is because of noise more than anything else. Other reasons that you would use an aftermarket cooler would be that you...