Here is an interesting note, and why I used the oil cooler from a turbo charged RX7 from the 80's...
The Wankle motor has few moving parts, but those that do move, have some interesting oil needs. The "rotor" is a 3 sided piston that spins around in a elipical orbit. This creates quite a bit of friction, and being so large, it has to deal with lots of heat from combustion too. The only way to get the heat out of a wankle is via the case that surrounds the rotors, or to use oil to transfer the heat out of the rotors. (What Mazda did to solve the problem, especially since there is quite a bit more heat on a turbocharged rotary than the NA versions of similar performance.)
On the TurboII engine, they installed a HUGE radiator style tube and tank, welded up aluminum oil cooler with a built in thermostat. (Awesome!)
On the lesser wankles, they have water cooled oil coolers that work pretty well too however.
My point is, OIL is not just a lubricant. It is also a very important way to transfer excess heat out of the motor.
I'm sure Jdub can go on about this subject for hours, but oil needs to operate in a certain range of tempature to be most effective.
Too hot, and you break down the oil, and it becomes too thin, oxidized and burns off leaving deposits etc.
Too cold, and it is hard to pump, retains water and that can cause problems as well.
So, you want your oil cool, but not cold. (Above 180f is good, and below 250f max is what I've been told, but I might be wrong.)
The T-stat on the Rx7 cooler opens up at 180. Actually tested it in a hot sonic parts cleaner.. works great.
I have done a less scientific test awhile back. It was very cold day, about 10f. I had driven for a few hours, and just to see if the cooler was doing anything at this very cold air temp, checked the end tanks on the cooler.. No supprise, the oil fitting side was too warm to touch for more than a second, but the other side, where oil should not have been flowing much on a day like that, was only slightly warm... Perfect in my opinion.
I have also checked it on a hot day, in traffic with the AC going, and the tanks are both super hot. (I do not have a oil temp gauge, but I'm sure it is cooler than the stock setup would be, but don't know how much cooler... but since both are hot, the thermostat is open, and flowing oil throughout the cooler v/s bypassing it.)
OK, so what's my point?
DO NOT DITCH THE COOLER.
Get a bigger one, but if you do, get a thermostat for sure. (Unless you live in weather that is never colder than say 75f, and I've seen snow in Mexico, so just living in the South does not mean you will never see cold temps.)
Here is where I mounted mine. (The RX7 cooler is tig welded at very small points via the bracket on the end tanks to my FMIC end tanks. About 1square inch of surface area at the most for thermal transfer, so minimal in my opinion, and it made mounting the oil cooler and FMIC easy, so it's worth it.) The oil cooler is in the airflow from the upper grille, and the FMIC is in the lower grille air flow. Note the in and out fittings on the right side end tank,a nd the nut that holds the thermostat in place on the tank as well. A custom center support is needed for this series of mods. (I bought mine for 30.00 off Ebay, and then coated it with thermal dispersant. It was pretty corroded, but so far, has not been a problem. I have seen cleaner ones for about the same price. Make sure you clean it out very well BEFORE you run this into your engine. Any crap in a used oil cooler will go straight into your bearings.)