If it cools while driving and overheats while idling then your problem is airflow. I would look into a new fan clutch. When they go out they cause you to overheat at idle because they aren't pulling as much air as they are supposed to.
NAPA part number 272310 is an upgraded one that will pull more air then the factory. Do your self a favor and don't tell them what it is for just ask for the part number. The counter jockeys will tell you it doesn't fit but it fits fine.