AMD recommends that you water cool your 9370 processors and above. AMD sells a version of the CPU that comes with a water cooler, part number FD9370FHHKWOX. Like you, I did not purchase their water cooler.
I've tried the Corsair H80, it cooled just slightly better than what you can get with air. The radiator just isn't big enough, however, you can add a second fan on the outside of your case to increase the air-flow. My son system has this configuration, which greatly improves the efficiency of the H80. For me, it still wasn't good enough. I ended up with the Corsair H100i. This thing keeps my CPU very cool. I'm not overclocked.
Good luck!