Allow me to revise my statement:
It depends how much you increase your voltage in order to achieve those clock speeds. At 1.5V, no, you couldn't have stable temperatures with the stock cooler. However, it's not uncommon for those chips to overclock into the range you're talking about without any voltage increase at all, in which case your stock cooler would do fine.
By the way, are you aware that 40C is 104F? I doubt that's your room temperature.