Sounds like the Kia acts like the older GMC overdrive. When towing it finds OD when the load lightens and drops to "third" when it has to pull. Does the "power button" disable the OD? If so, I would use it. If not try leaving the tranny in 3rd. It might seem like you would use more gas, but really, without the shifting, you dont. And yes , the tranny cooler is a must.
(I pull a 30' travel trailer in the mountains with a 88 suburban, on any grade, it has to be out of OD!)
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2000 KIA Sportage 4x4, Sadly Smushed! Now a 2001 Cheep Jerokee. 3" Rough Country Lift, 255/70/16 General AT2's
http://www.cardomain.com/ride/2292811