It was suggested that you do not run the cooler lines through the radiator.
That would be a mistake. The trans is designed to run at a specific temperature range too cold and it will not operate correctly and parts can wear out faster. Too hot and you have similar issues. The radiator warms up the trans and keeps it in the proper range. There are even thermostatic valves for trans coolers that bypass the extra cooler if the trans fluid is too cold. That would be the way to go to keep your trans in the proper temp range
