I think you are thinking wrong...
If there is a restriction it is not holding the fluid in the cooler. The pump would be fighting to FEED the cooler the fluid, which would hold the fluid in the transmission, causing it to heat up. The restriction would cause the fluid to NOT get to and from the cooler in a normal rate and only cooling a very small amount of fluid. You may want to do more reading on restrictions on flow.
Prime example, the thermostat stuck shut on the car last friday night. Radiator was cold as the air, but the upper hose was hot along with the block, had there been a hole in the thermostat the RESTRICTION still would not have allowed the coolant to cool properly and would have held heat, as you are suggesting with the transmission cooler. Heat is NOT the issue.