I put over 300K on my GTP's stock trans without cooler... just fresh Dex 6 every 50K and only somewhat abusive driving.
Trans temp stayed fairly close to engine coolant temp, as you might expect.
When I played with a stock 9C1 trans cooler, got about engine coolant temp -15* max (in line with rad)
Now with my Impala, I have a standalone cooler only with no radiator cooling... fluid hits about 160-170* max, perhaps runs too cool in winter but I have experienced no issues.