They are ok if you dont want to OC, but check the temps just incase its not doing its job. You can check in the bios, download speedfan, or everlast they all will tell you your cpu temp.
Yeah, it should be okay. However, make sure you take off all of the thermal pad and use some quality Arctic Silver 5 instead, so it is easier to take off if you do plan on getting an aftermarket one.