Gen3 auto box?

I don't know the true answer to your question, but my complete guess would be it's not possible or worthwhile on the Jimny.

I had a BMW320d as a company car and in standard form you could already select performance modes, ECO, Sport etc which changed the way the car performs, so it's already loaded with sensors and electronic tricks and the supporting hardware.
One of the reasons I purchased a Jimny was to get away from electronic gizmos, so I consider it to be "simple" compared to the BMW, so not sure changes to the ECU (if possible) would achieve any results.

But I could be wrong, hope not, I like the simple nature of the Jimny.

I do see what you mean and it's an interesting question I can't answer.

Extra coolings a good idea if towing a lot as most stranded caravan owners have overheating auto boxes on sunny days, it's something I have seen quite a lot. Ironically on Audi and BMW cars, but I guess all makes of auto boxes are susceptible to various degrees.

Have fun.

Mike