Well, here is how the stock CVT cooling system works. Oil is picked up from the sump by the oil pump. Then it's fed into the valvebody so it can split the flow to hydraulics (clutches, pulleys, etc.) then another low pressure circuit is used for lubrication & cooling, about 75 psi or so. This then hits the oil filter/cooler, then hits the CVT belt injector and roller bearings. That then falls into the oil pump and it starts all over again. IF you run an external pump and cooler, you are simply running a parallel circuit that is ONLY dedicated to cooling. There is ZERO lubrication in that circuit because it's not tied into it. This works because the oil pump can now draw from the cooled sump oil which will help it out if all other things are equal.
Follow me on this guys, OIL FLOW is what keeps the CVT alive. When you replace the clogged oil filter on a CVT......it doesn't tend to overheat because you have increased oil volume to extract the heat. I did that and AMSOIL and I could not get it to hit limp mode when previously it would do it almost every time without mercy. I'll preface that it was mainly the wrong oil fluid LEVEL that caused overheating and cavitation, but the higher oil flow definitely helped even better with oil cooling. When the CVT wears out, then it overheats no matter what you do. I'm not saying this will solve all problems, but how many guys have their oil filter in perfect condition & their CVT fluid levels perfect? I guarantee this isn't a common condition so you have to be meticulous about that and the CVT oil level has to be bang on.
Hopefully that's clear, just because you slap an external pump on does NOT mean you increased oil flow to the things generating heat. If I did that and drastically cut the lubrication circuit flow for the lubrication circuit, the entire CVT would die very quickly even with an external oil pump and big cooler. The CVT oil pump has to push large volumes of oil flow in the lube/cooling circuit just to keep the belt and bearings alive, cooler is better but oil volume matters too.
Here's another one: Too cold and the oil pump starves and cavitates because the oil is too thick to pump.....very bad. Too HOT and the oil level rises due to thermal expansion and the belt whip aerates the sump oil.......and cavitates the pump, and you lose belt pressure. This is why when you nail the oil sump levels perfectly........magically the CVT stops overheating and whining. I live in Chicago so maybe the western states things are different.
It's possible a slug of air in an external oil cooler that dumps oil directly under the oil pump pickup might aerate the oil. I think it's B.S. but I haven't tried it. The CVT belt itself is churning the oil like mad and normally this is OK as long as the oil level is bang on perfect. This is the primary reason the oil pump cavitates but thick oil can do it without any air in the oil sump, so can a stuck oil pump flow relief valve which is it's main job to control pump cavitation. This is my point, there are many things in the CVT that can fail over time that will overheat it, this is a mechanical problem.
Why that setup didn't achieve it's goal? It was a false idea that reducing the heat would somehow magically increase belt traction. Heat does cause slip due to cavitation, but that's not going to increase the belt traction beyond normal levels. You want the oil temperature not too cold and not too hot, so I'd say that 194*F is a pretty darned good target if I had to pick one.
I'm not saying the external coolers aren't needed. I'm saying lot's of times it's a crutch for an existing problem. Fix the problem first......then add the cooler and you now have an even better setup.