Buying the best computer case is not a guarantee of optimal cooling. You will still need to fill the fan slots with good hardware, at the very least. You might also want to provide a fresh dab of thermal paste for your processor. Lasting, consider replacing the stock CPU fan with a Corsair H60.
This is a liquid CPU cooler that can give you superior performance without annoying you with noise. Since advanced processors are incredibly expensive these days, you will want to protect it with the best heat management solutions you can find. This one fits the bill.
The H60 has a 120mm fan with a high static pressure to noise ratio. It also comes pre-filled with liquid to make setup as easy as can be. Users will never have to refill or prime this system. Installation is simpler so you can put it in and start gaming right away.