While my 6.0 screams and sucks gas at 4,200 rpm, that is the engines sweet spot on steep grades. I have never had issues with engine Temps, but do keep eye on transmission temp. The engine is made to handle the rpms. On steep grades I found it is best to lock the transmission to third gear on the steepest grades and maintain the peak torque at 4200 to 4500 rpms and I can maintain about 50mph on 5 to 7 percent grades with my 12k fiver. The trick is to maintain rpm, be patient and not allow the transmission to jump between gears or downshift. With the 2004, you may have, or will have a bit more of a challenge without the 6sp transmission in the newer models.
Some will say get a diesel, but that is not pertinent to the OP questions.