I had the exact same problem on my 2002 Export CRD...battery light came ON!
Owner's Manual said check Alternator and Battery.
Took it to have these items tested...no result!
Found some Wiring Diagrams for the 2002 KJs and ended up finding that the Battery Temperature Sensor under the battery was missing ground on one end.....the ground went into a splice in a big loom somewhere....I added my own ground!
You can remove the battery and remove the Temp Sensor underneath.
Measure the resistance of the Sensor at room temperature.
Heat up the Sensor with a hairdryer or incandescent lamp and you should see the resistance change.
The early KJs had this Temp Sensor fitted...supposed to slightly adjust the rate of charge by feeding Temp Data to the PCM/ECM.
Later KJs they dropped this sensor.
Most likely you have a wiring problems...download the 2002 KJ Service Manual here, Section 8W has the wiring diagrams.
www.colorado4wheel.com/manuals/Jeep/KJ/
The one side of the Sensor should go to ground...add your own ground to this side of the Sensor before climbing into the wiring!
The page you want is 8Wa-20-2. The BK/LB wire means Black wire with Light Blue stripe...tie this wire down to chassis and see if it fixes your problem....don't cut the wire...strip some insulation off and add a wire to the exposed copper and ground it.