From the Hayden Web page:
Should the cooler be installed before or after the radiator?
Answer: We recommend installing the auxiliary cooler after the radiator to return the coolest fluid directly to the transmission. Installing the cooler before the radiator will still provide additional cooling and may be necessary in some difficult-to-access applications.
Can you over cool the transmission fluid?
Answer:
Some transmission problems really are unique to the cold weather while others get worse. Metal components contract as they get colder which results in component mates loosening up, parts wearing quicker due to friction from reduction in clearances between components, and can develop leaks from shrinkage and hardening of seals and gaskets.
The ideal operating temperature for a transmission is 180°F. The viscosity of transmission fluid changes and gets more viscous at lower temperatures. As the transmission fluid (ATF) falls below 32°F, its viscosity becomes significantly higher, restricting where it can flow to lubricate the internal components of a transmission, leading to premature wear. The use of synthetic ATF fluids is recommended where its viscosity at cold temperatures is lower than petroleum based ATF fluids.
It is critical in extreme cold conditions to use the original equipment cooler in series with an auxiliary or
by-pass cooler and allow the vehicle to warm up before driving.
Hayden Transmission Oil Cooler FAQs