The predominant American design would be to have an ATF type of tube reservoir that goes into one of the end tanks in the radiator. I am not sure if it is to bring it up to temperature quicker or for cooling. I do know overly cool ATF doesn't allow the torque converter to lock up and on some it won't go into overdrive until it reaches operating temp. I tow a 5000lbs trailer every couple of weeks (O/D off), and have 305,000kms+ on odo.
My suburban has both, in-rad, and I have a radiator type factory installed 10in cooler in front of the rad. I have also installed a in-line spin-on filter just below the fan shroud which 'sees' a lot of air movement off the fan. I do a drain/refill 4L+ every year and the trans still shifts like new, & the ATF still looks bright red and smells new. ATF is cheap, and the infusion of new fluid is key to its longevity as heat is the #1 killer to auto transmissions. If the auto trans has basic cooling setup IMO dex3/dex6 dino with 1/4 to 2/3 sump changeout every year will provide better longevity than full synthetic once every few years...and cheaper too.