On current Chrysler trucks and Jeeps, synthetic 80W-140 gear oil (with friction modifier if needed) in the axle, is part of the towing package.
About 15 years ago Chrysler was using engine oil in stick shift transmissions. This seemed like a much better idea than the muscle car fill of either ATF or 90W. I've been using engine oil ever since in my street cars. They shift great like this hot or cold.