Chip, for the gear boxes I have been using a thermal gun to check the temps, I do not have full time temp probes installed.
With ATF running fairly hard empty I was seing about 140* with about 80* ambient. With the Mobil 1 installed I dropped to 110-115*. I have not done enough towing with any weight of consequence to have a solid number, but from what I have seen it is slightly bigger of a differential in temps, maybe as much as 40*. The transfer case does not get all that hot in any circumstances that I have found.
I put the motor oil in so I would not need a transfer case under warranty, but you do have a point. Isn't the Amsoil 5w-30 red? You could also dye the motor oil with a teaspoon of hydraulic fluid dye, but I think if your warranty is that important to you that you should just fill it with synthetic ATF.