Understand that your engine needs to rev to go up hill; 4,000, 5,000, or higher RPMs are normal. The engine is designed to run that way.
Use the tow/haul mode on your transmission all the time. When desending a grade be in low gears that allow you to not need the brakes very much. Again, the engine will be turning a lot of RPMs as you descend a grade in a low gear. This is normal.
If your truck is running hot, turning on the cab heat will help. It sounds counter intuitive but it works. It essentially give the engine heat somewhere else to go.