The first thing to consider, is what is the actual temp of the engine when the fan comes on. You can check that with an infrared temp gun. Point it at the area around the base of the thermostat housing. That is where the temp sensor is, too. Do that after a cold start, and while it's idling, keep an eye on the infrared gun, pointing and checking it every 30 seconds or so. If the fan comes on before the temp reaches about 215°F, the temp sensor may be sending a wrong signal. The fan should stop when it cools the engine down to about 195°F.
2008 JKU Rubicon