Tom,
The radiator in your car has two coolers. One [as normal] for cooling the engine, keeping the coolant at a set temperature, and another smaller one in the left corner.
This is the part of the rad that keeps the tranny oil cool.
Being an early model car, your oil cooler will have the filter inside that caused trouble, and it's built in and can't be removed.
This filter tends to catch a buildup of dirt when there is no canister filter in the oil circuit. In turn this reduces oil flow, so the tranny can overheat. That is why you should take ob-au's advice seriously. It is difficult to do a reverse flush of the rad cooler properly, and when I say properly, I mean without dislodging some of the gunk, which might later travel back into the tranny and block some small but critical oil passages there.
There is an awful lot of threads in the history here which will tell you how to do this if you run a search. As you are a newbie, and learning the mechanical side of things, I don't want to worry you too much, but if you make a mistake with it, it could cost a lot of money by killing your tranny. If you are unsure how to reverse flush, get a tranny shop to do it for you, and don't forget to connect in the proper filter when you are doing the job.
Best of luck with it,
Joe