2005 Dodge Ram 1500 how hot should your rear end get pulling a 3,140 lbs camper?

Hi, I cannot say I've ever felt a rear differential after driving - or towing. There is also no "specification" about rear differential expected temperature. Your vehicle is rated for what it's rated - gross vehicle weight and towing capacity information should be printed on the placard at the driver's door area. Verify this first. You also should check the influence of "tongue weight" of your trailer versus maximum towing capacity. If your trailer has an abnormally high amount of tongue weight, it could negatively affect the rear axles. See a local shop near you to discuss specifically related to your vehicle and concern - work together to find a solution! Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops