Oh, c'mon, you weren't this specific. And I was. A 240mm rad is large by normal standards. Sure, a 360mm one is larger, but also usually not needed and you are likely to run into clearance issues.
I mounted it outside the case. Lots of cases have little cutouts to facilitate this. The fact you are sucking hot air into the radiator is probably not helping you.
360mm isn't needed, unless you want it to be quiet...