To be clear, I understood the setup and appreciated the dry humor of it. I was just peripherally curious, as an engineer, whether even theoretically speaking the Clarity's mechanical ICE transmission/gearbox/whatever even contains any oil or whatever that could possibly be cooled. That is, whether the suggestion was just silly, or literally impossible.
Probably not literally impossible but likely practically impossible or at least very difficult since there is not an existing external fluid loop that could be tapped into so you would have to attach something to the drain and fill plugs. Adding a cooler to a system that already has an existing external cooling loop is a walk in the park by comparison.
Normal automatic transmissions have factory installed coolers, essentially a small radiator, which on passenger cars is typically built in to the main radiator although they do not share fluids. The reason that only automatic transmissions have a cooler is because you are not really trying to cool the transmission itself you are trying to cool the transmission fluid. ATF is not only a lubricant it also acts as a hydraulic fluid, and hydraulic fluids are more susceptible to heat damage than lubricating oil, combined with the fact that in an automatic transmission the fluid is subjected to a lot of stress and heat build up as it does its job of changing gears and applying driving force through the torque converter. Manual transmissions only use lubricating oil, and the oil is not really "working" it's just being splashed onto the parts to provide lubrication. So manual transmissions do not need fluid cooling, at least not at the passenger car level or even when towing a trailer with a pickup truck.
When someone refers to installing an automatic transmission cooler what they are really talking about is installing another cooler that will be used in addition to the factory installed cooler, so that essentially the transmission fluid will flow through two separate "radiators". The additional cooler is usually placed in front of the AC "radiator" (condenser) so that air flows through it first before passing through the other radiators including the factory cooler. Bypass hoses are installed which redirect the ATF fluid so that it flows through both the factory cooler and the aftermarket cooler.
Even though a supplemental transmission cooler can be added to any car with a normal automatic transmission, it is normally only needed for high power applications like heavy towing, especially if you will be towing in hills or mountains.
ATF fluid can also be used in other applications, in fact for many cars ATF is used as power steering fluid. In heavy duty applications such as performance cars some people add power steering coolers. Cars don't have built-in power steering coolers, but since they have an external reservoir and a pump you can tap into that line and run the power steering fluid through a small radiator.
Clarity uses ATF fluid in its "gearbox" likely for clutch purposes, as well as of course for lubrication. Presumably even if towing the ATF fluid won't get excessively hot, but even if it did there is no practical way AFAIK to install a cooler for the ATF fluid.
