If it is the original fan clutch it is probably toast, and is mostly freewheeling on the shaft and not pulling air with any power. If that's the case, then you are getting very little airflow at idle. When you're in motion there is airflow, and you have no problem maintaining you temperature - that indicates the your radiator, water pump, thermostat, etc. are functioning well enough.
The usual test for a fan clutch is to start with a dead-cold engine, and give the mechanical fan a spin with your hand, noting the resistance you feel. Then run the motor until it is good and warm (190 degrees or above), shut it down and immediately pop the hood and spin the fan again. When hot it should have significantly more resistance than when cold, since the thermally actuated viscous coupling is supposed to "grab" the fan shaft harder when warm. If there is little or no difference in spin resistance between hot and cold, that indicates a worn out fan clutch.
In my opinion, the test is hard to use conclusively without having experience with how viscous fan clutches should feel. But it is usually advisable to replace it anyways with the symptoms you describe. It is not an expensive part (less than $50), but it is a slight PITA to R&R due to the lack of space between radiator and fan, and the fact that the one-peice fan shroud cannot be removed entirely from the car until the fan (or radiator) is removed, which makes removing the fan mounting bolts annoying.
Also, many people upgrade to a ZJ ('93-'98 Grand Cherokee) Heavy Duty Fan Clutch, which has a more agressive viscous coupling. It will spin the fan faster than a normal clutch, which increases airflow but robs some power and fuel milage (at low speeds at least). It's a good idea if you do a lot of hot-weather slow speed driving.