Does it matter which side of radiator the transmission lines hook up to?

With an aux cooler..... I run the rad cooler first then the aux cooler in series. My theory is that the rad cooler will cool it to coolant temp, then the aux cooler will cool the trans fluid below that. If you run the aux cooler first, the trans cooler may in fact warm the fluid back up to coolant temp.

I may be overthinking this....