I've told this story before.......
Back in the old Compuserve days, I was working with a guy who regularly hauled a large horse trailer over some mountains. He was running a one ton Ford, still in warranty.
The Ford dealer had rebuilt his rear end twice, and the third time, replaced it entirely as one unit. Problem was, he would get about half way across, and start seeing smoke because the oil in the rear end had gotten so hot it was boiling out the vent.
He would pull over, let it cool, and go on. But, a few trips like that, and he would start got get bearing noise and it was time for a rebuild.
I was talking him through installing an electric temp gauge so he could watch his oil temp in real time, and pull over and let it cool before it got too hot.
One of the guys on the forum kept suggesting changing to Amsoil. This was back when synthetics were new, and we all were suspicious of them.
The temp gauge pretty much solved the problem, but now he had to stop several times per trip. Finally the Amsoil guy, who was a dealer, offered to send him enough gear lube to replace his oil for free.
About a month or so later, my friend posted up that he was still using the gauge I had helped him with, but had no had to stop since changing oil.
It just never got too hot anymore.
My '79 F150 had bare metal floorboards, and an NP205. After a hard run on the highway with 12.50-33s, I could feel the heat coming up through the floor.
I tried to check the oil once after a run, but, like you, did not want to touch the casing. Not sure if it would have blistered me, but I did not want to experiment.
After the rear end report, I hunted around and finally found some Amsoil. This was probably 1980 or so. As a result, I could not tell you the weight, but it was gear lube, not ATF. Probably 75W90, or something close.
After the same run, same weather, I could lay my hand on the case. It was not cool by any means, nor all that comfortable, but I could hold it there.
After that, I switched all oils to Amsoil. And have been running it since.
Does it cut down on friction? No doubt. Does it save gas? Technically it pretty much has to. The heat you feel is created by the torque of the engine being converted to heat instead of motion. Less heat, more efficient driving. Does it save enough gas to pay for its self or even be noticeable? Almost certainly not.
So, why do I run it? I don't mind doing mods or improvements to my vehicles, but I hate replacing worn out parts. My '89 F250 is 30 years old, has over 300K on it, and has had no lubed parts wear out.
The engine was replaced at 200K, but still had 35lbs of oil pressure at idle, good compression on all cylinders, and used no oil.
But, a new water pump seized up at speed, snapped the shaft, and the heavy fan took out the radiator, bottom rad hose, and dumped all the coolant out in seconds.
I stopped in less than a minute, but with no water, the block just sat there cooking even though it was not running.
After that, I started getting coolant into two adjacent cylinders. Tried a gasket, no luck, so I cut my losses and went with a reman.
Before I tried to rig a cooler for your transfer case, I would grab either one of the instant reading meat thermometers, or an IR gun and check the temp after a fast run.
Then change to a good name synthetic and check again. I like Amsoil, but there are others.
Be warned, there may be another theory out there about the cooler temps.
I was on another forum a year or so, and a guy was having problems with his rear end temps. I suggested Amsoil, and another guy chimed in.
He said it would ruin the bearings and gears in his rear end due to heat if he went synthetic. I had to ask, if it ran cooler, how did the hardware get too hot?
He said that the cooler case was not due to the gears and bearing running cooler, instead the synthetic oil would not transfer heat like regular oil. Thus the case got cooler since the oil never transferred the heat from the gears and bearings. As a result, they would get hotter and hotter until they failed...........
Since this would require the oil to have the insulating properties of something like Styrofoam, I decided it would not be a good use of my time to continue to converse with this person......