My recently purchased 2005 4.7 4x4 has been overheating at idle. AC makes some funny noises and starts getting warm and the temp gauge goes from just below 1/2 to 3/4 in about 5 minutes. It goes back down to just below 1/2 once I start driving again and the AC starts blowing cold again. Could this be caused by the missing fan shroud?

 

absolutely!!!! my personal experience: Back in college days, my roommate had a blazer.... didn't have a/c so it was fine without the heat shield when driving around town. We went to the sand dunes, and it overheated half way up the entrance hill. We returned to the parking lot and proceeded to remove a shroud from another vehicle and put it on his... a fair amount of work with just an emergency tool kit (I thought we were wasting time). I WAS WRONG!! We went back to the dunes and had a great day with the gauge never getting over half.
So YES, I would definitely say that is your problem.

 

Most definitely yes.