Some have an internal transmission cooler & extra small internal radiator for that purpose.
tranny cooler lines or tranny cooler blew up inside rad
No, but some autos use the radiator to cool transmission fluid.It circulates within its own plumbing, and the fluids never commingle.
When changing transmission fluid you should run car on road a few minutes just to get fluid warm, not hot. Next loosen all transmission pan bolts leaving two in back and then take out the last front...
It should be red to dark maroon if it's brown or a yellow color it is burnt and should be changed