do you have anything blocking the rad or is it dirty? if its clogged with mud or something and air cant get through it, and it will over heat a little while wheeling, although its not advised to run hot you can. also it could be a stuck fan clutch... most jeeps have that problem at some point. and instead of pulling the head off it try the little things.

 

first : touch upper rad hose when gauge shows hot is it really that hot ....
second: remove thermostat observe if coolant circulates in rad
third : if so , maybe the rad is clugged needs cleaning ...pretty rare that a jeep overheats .

I use the electric fan only in big traffic or offroad otherwise , no fan at all

 

You know I had the same problem but in reverse. 3 thermostats in a row from Canadian tire that were stuck open so the engine wouldn't heat up, drove me up the wall trying to figure it out. Don't be too too quick to discount cheap new parts.
Make sure your upper rad hose is hot when the engine is, if it's not your therm isn't opening. Sounds like you replaced the rad so check the mounting bolts to the water pump. If your fan clutch is going it will sometimes shake the pumps housing loose.
How hot is it getting that your dad says its ok?