Transmission problems on 1995 Chrysler LHS

At startup and cold transmission won't shift into 3rd gear. If I come to a stop, turn off car, and back on, transmission shifts normal, including third gear. After car is warm, transmission shifts hard into third gear and seems to be shifting a little late. What could be wrong?

2 answers
the input out put speed senser is gooing out if not all ready out
No engine check light? Have auto zone do a diagnostic free if engine check lite is on.