I just noticed that you said that you have the stock cooler in the OP.
That "should" do the job in a non-OC'ed system. Check to be sure that all 4 mounting pins are securely fastened to the mobo. It is easy to push one in and think that it is all the way through when it is not, and the barbs at the end of the pin have not properly latched to the mobo. The best way to check is to remove the case side panel under the mobo and have a look. If you cannot see them that way, you'll have to remove the mobo from the case to see the underside.
You could also get an
Aftermarket Cooler (Link) .
Yogi