On the beach, it is very hot, and you do not drive more than about 10 mph. 10 mph does not create much air flow. The fans might be enough to keep it cool. It is hard to tell. You need lots of air flow across the cooler for it to be effective. For towing, it works great because you are moving at 65 mph. For the beach, it may not be as good. I would not use the JK to tow anything large.
I still think that a transmission temperature reading would be very helpful, in addition to the transmission cooler and the warning light. You could watch it as you wheel. If it starts getting hot, then you can turn around and go home or at least shut it down until it cools off. I view transmission temperature about as important as oil pressure, but you never get a temperature reading.
Regarding being in a remote location, apparently most tow trucks here in the South are two wheel drive. They do not do snow removal. Thus, they do not waste their money on a 4x4. Sounds silly to me, but that is the case. We have 200,000 people in this county alone. Thus, we are not too far out of civilization. It is nice to have less crime in a lower population density area.
'06 XK Limited, 5.7L, QD II, Black, 163K
'02 WJ Overland, 4.7L HO, QD, Inferno Red, 126K