Stock Cooler and 3570K should not be used in the same paragraph. Ivy Bridge runs hot, WAY HOT.
Either ante up for a decent cooler, or sell the 3570K and get a 3570
On a serious note 4ghz may be possible. Read some guides. I don't know what software you are using to stress test, so its hard to say.
Do yourself a favor and use a fixxed voltage, not "Auto". Using "Auto" voltage in your BIOS may send too much voltage to your chip, and being as you are on a crappy cooler - potentially get too hot and damage something
The 3570K TJMAX is 105C. I personally would not push much past 80C
Keep in mind after you find your stable OC threshold, normal applications should not make your chip near as hot as running Prime95 or similar.
For example, I am running a 3570K with a 30$ cooler master EVO @ 4.3GHZ.
During stress tests, I hit high 70C. During gaming for hours, I hit high 50C