There have been numerous threads about this in the past. You may want to do a search on it.
However, I've always taken it off the car, and filled it half way with water, then add half a spray bottle of Castrol Super Clean (the purple stuff). Then fill it up to the top of the neck with water, slosh around a little, and let sit for a few minutes. Pour out (not on your grass or garden), and repeat the process. Once you've done the second round, run a water hose through the neck in the direction air will flow, and let it rinse through for a few minutes. You'll be amazed at the oil residue and greasy grime that comes out. Once done, the thing will be extremely clean and certainly more efficient for cooling. Let it dry for an hour or so, before hooking back up to car. If you have compressed air, blow through it for a bit, to speed up drying.
Works great for me!!!