just my opinion but i would never use a cooler in the rad, It was a cost cutting exersize by the manufactorers in my opinion, Imagine it did leak water in the trans means instant rebuild, much better to use a stand alone cooler with 3/8" pipework mounted in a good air flow or assisted with a small fan. they are not expensive are they ?
Also cooling trans fluid with hot water can't be a great idea
Cool trans fluid usually means long life