Another thing that I read was a higher gear ratio produces more heat. IE; a 4:11 would run hotter than a 3:73 or 3:42
From a transmission standpoint, I believe a higher (numerical) axle ratio will allow the trans to run cooler. Not sure if you were referring to the axle temp or the trans temp. A lower (numerical) axle ratio requires more torque (from the trans) to maintain the same road speed, so in general I'd think the transmission in a 3.42 axle truck would run hotter than one in a 4.10 axle truck. Of course, the 4.10 axle would also be running at a higher speed, so maybe that tends to offset the difference due to torque. I'm not a cooling systems expert, so my opinion may be all wet.
I do, however, have one tool that may provide a more definitive answer. I have a program that simulates transmission thermal operation during one particularly severe portion of our powertrain endurance testing. I can change axle ratio in that simulation, and see what the effect is. So I ran the simulation three times, for a 3500 truck with 68RFE trans, at 35,000 lbs GCW, running in 90°F ambient. Now admittedly, you wouldn't want to run that truck with a 3.42 axle (in real life), but at least this gives us a comparison. I ran the 4.10, 3.73, and 3.42 axle ratios. Here are the results, starting in each case with a 180°F sump temp:
• 4.10 axle = Peak sump temp of 216°F
• 3.73 axle = Peak sump temp of 224°F
• 3.42 axle = Peak sump temp of 236°F
So it looks like my gut thinking was probably correct.