On the cars with the automatic, does the transmission cooler cycle coolant to the transmission via lines, or does transmission fluid get cycled into it's own separate internal radiator lines???

Reason I ask is because I may swap an A4 transmission into my car and adapt oil lines to the tranny cooler lines. My car just refuses to keep the oil at a comfortable temp and I need to do something to combat it.

It has its own lines that go into the bottom of the radiator.

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Awesomeness. You wouldn't happen to know the size of these lines, the size of the core for the cooler in the radiator would you?

Does anyone off hand know the size of the transmission cooler inlet and output lines on the automatic transmission?? Just looking for a line diameter, that's all.