The case has little to do with CPU cooling; you seem to be confusing terms; it can affect 1-5deg of overall system temps, but not a huge worry overall.
If you're not overclocking, any of the 'popular' aftermarket coolers will do. (even the stock one will, but might throttle on hot days)
Assuming you're not overclocking I try to find a cooler that has a 2nd appeal (aesthetic, performance, price, etc); as an example (i am overclocked; 2.6stock up to 4.2ghz) I use a Noctua C12P.
Some tests show the U12P to cool a degree or two better; but the C12P being a 'flat' cooler blows directly over the known to overheat PWM's and also slightly over the RAM too.
In other words; its a good CPu cooler and is providing other functions I like too.
So find one you like, and we'll try advise yay or nay.
I'm a fan of Xigmatek fans, and Noctua coolers personally (noctua fans too; but the price!)
Wherever you go in life, watch out for Scythe, the tackling IT support guy.
"I don't care what race you are, not one f*cking bit, if you want to be seen as a good people, you go in there and you f*ck up the people who (unofficially) represent you in a negative light!"