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Transmission Cooler Diagram

Often, external trans coolers are plumbed so that they replace the stock in-tank radiator cooler, but most OE and trans cooler manufacturers recommend retaining the factory cooler, using the external cooler to increase the system's heat-transferring capacity. Proper routing passes the fluid through the radiator cooler first, then on to the external cooler before heading back into the transmission.
Automatic Climate Control - Cool Transmission Tech

Often, external trans coolers are plumbed so that they replace the stock in-tank radiator cooler, but most OE and trans cooler manufacturers recommend retaining the factory cooler, using the external cooler to increase the system's heat-transferring capacity. Proper routing passes the fluid through the radiator cooler first, then on to the external cooler before heading back into the transmission.  View Related Article