I am suffering this on an older 2000 TJ, but even with my mileage it is not normal.
After shutting the engine try and touch the radiator core with a palm from the fan/engine side - in my case, the right (passenger) half of it is hot
while the left
(driver) side half cold
And this is a relatively new (10000 miles, 2 years) dealer-installed radiator, well filled with clean coolant, well draining to the expansion cup when hot.
Please share your further steps, let me know.
(I bet Chrysler shall know this problem)