4.0 should not be a problem with the stock cooler in either case.
The 3570K only gets very hot when the voltage is raised, seeking a maximum OC. @4.0, you can leave the voltage on auto. Maybe more.
But, I would buy an aftermarket cooer, regardless. A Simple tower type cooler like the CM hyper212 is only $30http://www.newegg.com/Product/Product.aspx?Item=N82E16835103065
It will cool better, and the 120mm fan will be quieter.
The backplate mount is much easier to install than the Intel pushpin mounts.
It will fit in either of the two cases.
You also could look at the Antec 300 illusion model, it is cheaper and will cool nicely.http://www.newegg.com/Product/Product.aspx?Item=N82E16811129066