2000XJ extended aux. fan run times

2000 Jeep cherokee 4.0. I searched for a few hours but didn't come up with an answer. The auxillary fan will continually run after the Jeep is shut off. Sometimes it will run for 1-2 hours. This only happens after running the A/C compressor. Will not do it if only overheating has caused the fan to turn on. Already changed out the temp sensor. Is the next step the A/C relay or am I missing something else. And no, I don't want to just put a switch on the aux. fan to turn it on/off.
Thanks guys

older xj's that had have that problem can almost always trace it back to a sticking fan relay it seems......

There's a fan relay in the Power Control Center, under the hood, near the battery. Look under the lid to ID the relay location. If after you've shut the engine off and it's still running, tap the relay with the handle of a screwdriver, and it should shut off. That's also a good sign that your relay is sticking. I had the same problem on my '98. The relay should be less than $20 from the dealer...