You probably can't get comfortable temps with this tiny cooler, if you want silence you need a big heatpipe based cooler. Go find an coolermaster hyper 212+, that should work passively. It should sell for 20$~30$
This is a Sempron not an i7 its not going to be generating nearly as much heat as those. At worst case the 15 dollar heatsink(including the fan) will work no problem. One of the reviews even said he ran prime95 and the highest temp his cpu got was 35c and he is running the 11 dollar heat sink.
You wanted to cool it without the fan, that puny little heatsink won't do it, even a low end graphics card will heat it up considerably. But of course it will work with the fan.