2002 Ford F-250 overdrive shifting

In cool weather it shifts fine but as soon as it has gotten warm out it does not shift into overdrive. I was told that the transmission needs rebuilt but I can't understand that it works fine in the cold but not as soon as ithe weather warms. Also it can sit all day in 70 to 80 degree weather and as soon as I start it up the trans temp gauge is already up to operating temp. The lock out button does flash on and off without touching it, and will not go out by depressing the button.