I'm guessing here...a WILD guess at that, that maybe your car is running the A340/1E transmission???
If so, these transmissions like to be cool.
The advantage of installing a separate cooler is that the trans fluid will be MUCH better cooled than in the stock installation, resulting in longer transmission life and, thus, les expense.
I am putting a 1UZ into a Cressida, which runs the A340E transmission and I had not even thought of retaining the stock transmission cooling...I'm going to fit the biggest 'cooler I can squeeze in there!
Hope this helps!