Welcome to the forums!!
I have a P3125 on my P/// 600E (see my sig below), and while it will cool the chip extremely well, the idle temps are usually just over ambiant.
I think the only way you will get below ambiant is with water cooling and/or a peltier. The P3125 is a great hsf, and is highly regarded as one of, if not the best P/// SECC2 hsf available.
You shouldn't have any thermal problems with one of these, I think. I know I don't. I am able to run Prime95, and Sandra CPU Burn-in simultaniousely, and my CPU temp never reaches 40c. (Usually tops out at 37 or 38c)