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Yes, there's a liquid to liquid heat exchanger inside the trans. Coolant is supplied from the radiator to the trans. There is no external trans cooler and no way to conveniently install one.
The transmission oil cooler is mounted to the front of the transmission & uses engine coolant to cool the transmission fluid.
For general day to day use its ok. If you plan to do alot of heavy towing &/or in warm climate you may want to look into an adapter plate to allow fitment of a true ( external ) oil cooler.
Part # 3 is the trans cooler. Part 1 & 2 are the coolant hoses.