I don't know of any specific concerns that are specific to your Jeep, but I can give you a very good Ideal as to what you should do to check the system.
If it was boiling over into the coolant reservior, you are correct, the engine is overheating.
Your description tells me that you may have a cooling system thermostat that is stuck in the closed position and will not open as it should when the engine begins to warm up.
If you feel the radiator is plugged, you can check the flow of a radiator in this way.
While the engine is cold, simply take the radiator cap off, and with the radiator completely full, pull off the lower radiator hose. The Radiator should empty itself very rapidly. If the water flows out of the radiator very slowly, then you are correct, the radiator is restricted. If you are able to visibly see down inside the radiator with the cap off and the coolant level low, you should be able to visually see corosion and lime/type of buildup that can cause restriction in a radiator core.
Replace the Thermostat, check the radiator flow rate as described above. Be sure to check the operation of the Engine Cooling Fan and Fan Clutch. Be sure that your Electric Cooling Fan/Fans are functioning when engine reaches just above operating temperature. Also check with A/C in on position. This should engage the condenser fan if equipped.
While filling the radiator if you are able to actually look down inside of the radiator, when the level reaches the top radiator tubes, you should be able to see circulation as the new thermostat begins to open. This will also confirm that the water pump is pumping coolant as it should.
Check that the thermostatic fan clutch is pulling air through the radiator by feeling for air movement behind the fan blade. Do this check carefully staying clear of moving engine belts, fans and hot hoses.
If you have any questions, please feel free to ask.
I have explained briefly exactly the way I check a vehicle that comes in for an overheating condition.
There are two more thoughts I have.
Possibly the water pump empeller is not doing its job. It may pump coolant and then not pump coolant. This is a very difficult problem to diagnose because it will sometimes only pump enough coolant to keep the engine cool when it is not placed under a heavy demand.
If I thought this was a problem, I would completely remove the thermostat and reinstall the thermostat housing and watch down the radiator to see if it is pumping coolant briskly. You should see flow with the thermostat removed from the system.
And last but not least, have the engine checked for possible blown head gaskets. Sometimes they are just beginning to leak a little and the overheat only happens when the vehicle is placed under a heavier demand.
Be sure the All the cooling fans are functioning properly and coming on when they should. Check the flow rate of the radiator. See if the water pump is working, and last, check for blown head gaskets.
One additional note: The radiator cap can make a vehicle appear to be overheating if it does not create a good seal when installed on the cooling system. BE sure the Jeep is indeed overheating. You can have the cap checked or simply replace it with a quality new cap.
I hope I have helped with your overheating concern.