Hi Phil.... Dont do it !! Make a loop to main cooler to avoid contact between liquid and atf oil is not good. Oil of ATF need certain temperature. Find the new version of motor cooler that solve the problem...
I hope you understand

i think that is the temperature you have when follow the measurement level of oil...
175 °F is the optimal operating...

This doesn't make a whole lot of sense to me. A radiator is not, by design, a bi-directional heat exchanger. Even though you can overheat the tranny fluid if the engine coolant is hot and vice versa, it is not designed to be that way. If operating temperature was critical to tranny fluid, a type of thermostat would most likely be used in the system.

Also, tranny fluids today can still flow at something like 50 degrees below zero.

The only reasons you check level at operating temperature is that you need to make sure the torque converter and the rest of the tranny cavities are full of fluid. Also, tranny fluid has more volume at operating temperature (it expands some).