1999 Jeep Cherokee trans problem

I have a 99 Jeep Grand Cherokee 4.0 4wd with 120k. When you take off from a cold start the trans hangs up in 2nd grear for about 5-10 seconds and then it will eventually shift into 3rd. After the first take off and after it goes through all the gears it will shift normal from 1rst to 4th with no issues. Also if you let the truck warm up in the morning for atleast 5 minutes it will shift perfectly normal as well. So it seams that this problem is only when the truck is cold after it warms up its fine. The fluid in the trans. Was red and did not smell. The filter looked old and the plastic case was brittle. I changed the filter and put new fluid in it. The same problem still exixts. Any thoughts?