You may be right on the thermostat. It may just give you a bit of extra buffer in terms of having a engine that is 10 degrees C colder before you start going up a hill with the trailer.
In the Netherlands we don't have hills and extreem temps no
And the 1KZ engine is not common here, specially not with automatic. I know one guy who was very negative about the engine, not about the power and such, but about the cooling issues.
However, the 2L and 3L engine (codes) can get cracked heads to if the cooling is not sufficient.
And from the Netherlands I can drive through France, which I did in a heatwave. So with a loaded camper van going up a hill with 40 degrees C outside... So I know the feeling.
However mine did not overheat, even though there wasn't nearly enough coolant in the system. I found out about that later, couple of days after holiday, when I noticed that all the coolant was thrown out via the radiator cap. And it started overheating in normal conditions. Then I replaced the cap, the hoses, and flushed the coolant, and didn't have any issues.
By the way, I can clearly hear the visco fan engage a lot of times when I'm trashing it on the highway. That means driving faster than a 100km/h, like 110 or so. That may not seem like fast, but my van has a high roof, and the 2L engine has no turbo, it needs to work hard.
But as said in one of the other topics. I think the 1KZ has a small design error which can lead to a cilinder not being cooled enough.