2003 4.0l Ranger will have the 5R55E transmission.
Good read here on problems with that transmission: Common Problems for The Ford 5R55E Transmission: Do You Know What They Are?
And for sure add a 2nd trans cooler.
There are some videos on fixing problems along with other information
Symptoms on automatics vary too much to say "yes, that's the problem", you are there so only you know all the symptoms, so read a few articles that others have posted and may be it will ring a few bells on your problem.