reply not to you but to other users which may encounter same story -
if 1600X would not be oced at all, and if you would never do any stress tests - you will be gold even with a6 9500 cooler,
the reason of that is simple, i have stable I7 6700K @ 4.8GHz @ 1.45V with Hyper 212 EVO combined with 2xR9 390 trifan gpus, i can't do any stress tests at all, instant freeze due to 100C, but gaming with CrossfireX - easy
another reason is that quote from a bit of googling - "I ran my 1600x @ 3.8Ghz with 1.2 volts on the wraith stealth while I was waiting for my AM4 bracket, max temps hit around 68 in pubg, idled at 27C.
It’s more than enough if your case airflow is OK.
I’m now running an EVGA CLC on it instead, now I’m getting 4Ghz @ 1.275volts. Temps max out at 49 degrees in pubg now, Idle at 23C. I also have the Hybrid 1070 so even less heat in my case going around, it definitely helps hugely.
IMO the extra 200Mhz and 20degree lower temps are not worth it, for the average user it’s almost impossible to tell the difference"
you could say - "well that's wraith stealth, of course it's much better" yes and no, wraith stealth is on 65TDP versions of ryzen only, even if a8 9600 cooler is let's say 20C worse (just a random example which sounds way too bad to be true) , you still will have a max of 88 and will gaming just perfect