Note" not all models of the 5AT are affected by all of the design flaws, there are variations and changes through models and years. Some models of 5AT with all these condition were used from 2001 to 2006.

There are a few design flaws and design decisions that create problems for the Torque convertor and cooler circuit. Honda uses a three-path TC flow circuit that incorporates a converter bypass valve, as a result it is sensitive to outside variables such as restricted heat exchangers, filters and cross leaks. Add to this an undersized pump and any restriction in the cooler circuit can cause the TC check valve to open and reduces apply pressure. Too much restriction and the check valve may position some valves in a partially blocked position. Without internal modifications (during a rebuild) the TC will overheat

Lower pressure and design shortcomings mentioned above can start to destroy the torque convertor as this transmission ages.

Apart from traditional heavy load and hill climbing conditions, transmission fluid temperatures in this 5AT can really start rising in stop start traffic. ATF flow through the TC is on the edge of being compromised, especially when stationary and in gear (D, R etc.) and fluid that oxidises and ages quickly like Z1 make the condition worse whereas high-quality synthetic ATF will be helpful. Oil viscosity is also an issue in higher temp climates and an overheated converter is even more likely. At idle - below 1000 RPM - and in gear, oil flow can almost shut off through (bypass) the TC and cooler circuit. This is reported to be one of the main reason for the numerous problems of early torque convertor overheating. TC output fluid temperatures of 360F have been measured under this low flow condition. 

In very cold climates with easy driving conditions an external trans cooler may not be needed, but if you tow or drive in hilly terrian then it may be needed -
Cooler testing recap. In warmer temps an external cooler should be considered if driving conditions are not favourable. If you use a cooler use a low restriction unit, consider removing the OEM unit and be careful with routing ATF lines, no tight bends, high quality hose and quality transmission cooler. Whether you add a cooler or not, here is yet another reason to replace that filter and keep the cooler path as unrestricted as possible.