The KJ was designed to use 5w-30. (5 is the cold weight, 30 is the hot )
Conventional or dino oils do not have the better cleaning/lubricating properties of full synthetics.
It is true that for better fuel economy, they recommend the 5W-30.
As an engine wears and has higher mileage, rings and other internal parts do wear so many may consider a good full synthetic "high mileage" formula like Mobil 1.
Fact, our KJ do run hot. On highway yesterday on my scan gauge reader, my temps were steady @ 205 F at 60 mph, when outside temps were only 59F.
Stuck in traffic in stop & go, temps climbed to 215F. Off road in summer things can really cook 225F+ !
If you are not going to cut vents into the hood, in summer it may not be a bad idea to run 10W-40. This really depends on driving requirements, and outside air temps.
In winter, I like the idea of a better flow rate offered by 5w-30 and have been using it year round with no problems.
I run 5W-30 Penzoil Platinum full syn and will use an oil additive LubeGard Bio-tech engine protectant. Jeep seems to like it and gets a bit better mileage with it.
Pulling a PCV line when the engine is really hot, will give an indication how much oil blow by your engine is suffering from. If it lots, a bit thicker oil may very well help.