Are you getting your reading from the MB bios or a program under windows? I'm using the same MB as you and under the MB bios the temps appear significantly higher in comparison to a program monitor under say windows.
I've also had the hyper 212 EVO on the i7 6700k and for me the problem was noise especially if I benched/stressed it the fan would really ramp up. While with the old i5 2500k this was never hardly noticed at all. The Evo will get you by on your i7 6700k but don't look for any serious overclocking.
My 2500k didn't really make much noise, if it did I heard it the same..and I had it over clocked at 4.2. I can oc using the features in bios of this board but I have not done so yet. I probably won't do it now. The h80i was on sale yesterday so I was thinking about switching to it.
Edit: Idle temps through Hwmonitor state about 27-29 Celsius. Under load while gaming for a bit it got up to 39-50. I guess it should be fine.
The mobo in bios says idle is higher and the gigabyte SIV app says it's kind of close to HWmonitor.