The stock cooler is the bare minimum for cooling and it will run pretty hot when under serious load. I would recommend getting a cooler and just playing it safe. Also, keeping it cooler will help prolong it's lifespan.
You can take a look at coolers like the Cryorig H7 or Hyper212 Evo as they offer some really nice cooling for not a whole lot of money.
Be sure to do the research on your clearance space inside your case and the size of the cooler.