It's more than enough for LoL, it'll run 60 fps constantly in Max setting on LoL and 35 to 60 run medium to high settings in Battlefield 3 1080p, depending on the map and player count.
The more players and Map detail and destruction, the more the game becomes CPU intensive.
The CM Hyper 212 Evo is a good cooler, I overclocked my i5 2500k from 3.3 to 4.4 ghz and runs below 60 celsius in CPU demanding games like MMO's. I think you can overclock your GPU's clock speed to gain more performance.