I need some clarification here... What speeds are you having transmission temps at?
From your previous posts I'm guessing the trans is only getting hot when you're at lower speeds? If so, you should be in low range specifically for this reason. At lower speeds, it doesn't have anything at all to do with TC lock up, but with the amount of slip (i.e. friction and heat) you're forcing the transmission to do by "lugging" it in high range. You need to take advantage of the gearing of low range.
Towing off road in low range is no big deal at all as long as your speeds are low. If you're in 3rd or 4th gear in low range, you need to shift back to high range. Also, unless you need the extra traction, there is no reason
not to run in low range with the CDL unlocked - less bind and less wear/tear.
Towing on the highway (at highway speeds) needs to be (and is only physically possible) in high range.
The CDL being locked or unlocked will have no effect on your transmission temps. Also, the CDL has nothing at all to do with the gearing in the transfer case - locking the CDL simply changes the function of your AWD transfer case (i.e. slip between the front and rear drive shafts) to that of a part time t-case that's been put in 4-high (front and rear drive shafts turn at same speed no matter what).
Window nets