Interesting to read the responses here. I've got an '07 5.9, pretty much same as the OP's truck. I put gauges on a long time ago and kept the truck stock for a long time. You will be amazed how hot the EGTs on this motor will get in stock form. I've had mine at 1425 when I chickened out. I didn't figure I could hurt it in stock form but that seemed hot enough, haha! Contrary to popular belief, downshifting and winding it up actually produces higher EGTs. I've seen the hottest in the 2700rpm range. At lower rpm the computer is programmed to not give as much fuel and it is virtually impossible to get EGTs too high by means of lugging with the auto tranny.
I really like having my gauges, just gives me a little extra info on what the truck is doing. Boost/Tranny/Pyro. As far as cooldown goes, think of it like this: How many people out there who nothing about these trucks drive the wheels off them and never let them cool down and they just keep going? I let mine come down to around 350, but if you're waiting for 300 degrees, you'll be waiting for a while. Seems like wasted time and fuel to do that.
Now, since I've put the Smarty Jr. on, my EGTs are much lower at WOT and towing, but they do come up higher down low now. With reduced EGTs that temperature is now inside the cylinder so I've made a lower EGT limit for myself. That's another topic though.