I got a stock 200 R4 and am putting cooler on trans. I live in a climate that does not get cold in winter. Can I put the cooler after the stock cooler? Or is that a no no?

 

Out of logic, I think that would be the better place to put it for maximum cooling in hot areas.

 

I put a cooler on my car this year, my local trans shop recommended I install it so the hot fluid goes through the aftermarket cooler then back through the original heat exchanger in the coolant radiator.
He recomended doing it this way to avoid overcooling the trans fluid, don't forget trans fluid just like all lubricants works best at the right temperature and this was a good compromise if I didn't want to go to the trouble & expense of fitting a thermostat as well.