I tried using an older cpu with no heatsink, and got hot fast (I shut the computer off as it climbed past 90C).  You need something to increase the heat-transfer surface area.  With the same cpu I have had good success using a low-profile passive heat sink.

I haven't had any problems with fans in the oil.  My guess is that the increased resistance is offset by the increased lubrication and cooling provided by the oil.  The video card fans seem to be pretty effective at moving oil through the heat sink.  The squirrel cage fans they typically have aren't much different in concept to an impeller pump.