It's not all that sensitive to viscosity, you can go to a heavier viscosity but it won't make it run any cooler. By the way it is 100% normal for a differential to run warm/hot enough that you can't hold your hand on it more than a couple seconds at the most.
There is a known way to help the gears to run cooler though, that's simply changing from a synthetic GL-5 gear lube to a conventional GL-5 gear lube. Yes that is true, your gears will actually run cooler when lubricated with a conventional gear lube which sinks the heat out better than a synthetic can. That's why gear and axle companies like Revolution Gear, Yukon Gear, Currie, and Dynatrac specify or require the use of conventional gear lubes to keep their warranties intact or to insure the gears run cool enough during new aftermarket gear break-in process.
Factory gears don't need to be broken in since their manufacturers pre-lap them so they're ready to be driven on when they leave the factory. Synthetic can be used for them. But for aftermarket gears a conventional is required during the break-in since it helps them to run significantly cooler during this critical phase.
So if you want your gears to run cooler, just switch to a good conventional GL-5 gear lube like Valvoline, Mobil, Torco, Castrol, etc. And if your Dana 35 has a Tracloc limited slip differential inside it, make sure the back label of whatever lubricant you buy says something like "Compatible with limited slip differentials" so it will contain the additive required by them.
And for any non-believers, here's one good source of information... John Currie. Contact him and ask why Currie started requiring their axle customers to run only conventional gear lubes. He and and others in the industry were surprised by what they found in the face of an unacceptably high rate of ring & pinion gear failures caused by the use of synthetic gear lubes by their customers.