Help with Mits. Challenger overdrive

I have a 1999 Mitsubishi Challenger auto that wont go into overdrive or stay in overdrive if it does go in. I have had it hooked up to a diagnostic computer which didn't pick up any problem and all other quick checks or other indicators seemed normal. There does seem to be a temperature component to it where if it runs a bit warmer it will shift up.

My mechanic, the local Mitsubishi Dealer and one auto guy all scratched their heads and while they had suggestions no one was certain and I can imagine a lot of time and money being spent on diagnostics if no one knows where to start looking. I wondered if anyone else has had or heard of this problem with Challengers or Mitsubishi?
A.