A Jeep radiator fan that runs constantly, even when the engine is cool, usually points to a stuck fan relay, a failing coolant temperature sensor sending a false high reading, or a fan control module that's telling the fan to run nonstop rather than cycling normally.
Under normal conditions, your Jeep's cooling fan only needs to run when the engine gets hot enough to need extra airflow through the radiator, typically at idle, in traffic, or right after you shut the engine off on a warm day. The fan is controlled by a sensor that reads coolant temperature and a relay or module that switches the fan on and off based on that reading. When one of those parts fails, the fan can get stuck in the "on" position and run continuously, even at highway speeds or right after starting the engine cold.
A relay stuck closed is one of the more common and least expensive causes, since relays are simple switches that can fail mechanically over time. A coolant temperature sensor that's reading inaccurately high, even though the engine is actually at a normal temperature, will also tell the system the engine needs cooling when it doesn't, and this is a common enough issue that it's worth checking early. On newer Jeeps with computer-controlled cooling fans, a glitch or fault in the control module itself can cause the same nonstop running.
It's worth knowing that a constantly running fan, while annoying and hard on your battery if it continues after you shut the Jeep off, is generally a safer failure than a fan that won't turn on at all. Still, it's not something to ignore, since it can drain your battery if you're not driving often enough to recharge it, and it may be masking a sensor problem that affects other parts of how your engine manages temperature.
If your Jeep's fan won't stop running around Ann Arbor, whether it's idling in your driveway or humming along after a short trip, it's worth having the sensor and relay checked before it drains your battery. Hoover Street Auto Repair can diagnose which component is causing it and get your cooling system cycling normally again.