Re: overheating issue
Water or H2O is a NORMAL byproduct of catalyst operation. Yes excessive water or "white smoke" can be an indicator of a blown head gasket it does not mean that its a head gasket issue.
When filling the cooling system have you removed the bleeder at the top of the front cover? If you didn't that is likely your problem.
Ensure your fan is turning on, I replaced my radiator like 2 months ago, it wasn't till it heated up and I found my A/C operation sucked when I wasn't moving, further encouraging me looking into it was when we were loaded up to go out of town, and the temperature started creeping up, the mechanical fan locked up and kept it from getting too hot, I then found the electric fan had come unplugged (never plugged in???)... oops. All is good now.
Head gaskets are not an uncommon occurrence on the 4.7l unfortunately. That may be what your dealing with. If your not externally loosing coolant and the cooling system is bled properly that is likely what is happening. a "block tester" from NAPA is like 50 bucks, you remove the radiator cap, drain a little coolant out of the radiator (you just dont want the level as such that it pushes up into the tester with the jeep running). stick the funnel in the kit on the filler neck then add the chemical that comes with it (its blue) up to the specified line, now grab the bulb that came with the kit and pull a some air out of the cooling system through the setup. If there are "exhaust gasses" in the cooling system the chemical will turn yellow. if that doesn't do anything start the jeep and run it through at least 1 thermostat cycle with the setup still on the radiator fill neck.
If it turns yellow the heads are going to need to come off and be inspected. If it DOESN'T turn yellow that does NOT completely rule out head gasket, unfortunately this test is NOT perfect. It is helpful for a clear failure though.
2005 Jeep Grand Cherokee - Gone but not forgotten!