Claude,
Your transmission problems could be caused by so many things. There are many tests and adjustments that can be done in situ without removing the transmission from the car, but they require hydraulic fluid pressure measurements, so some specific equipment is needed. The tests require the car to be on a hoist so the engine can be run with the transmission engaged (wheels turning), so if your engine is overheating this complicates things, because you would be limited how long you can run the engine and it will also overheat the transmission fluid as well.
I think perhaps the engine overheating should be tackled first.
Here's a link to a fault diagnosis list for the Torqueflite A-727-A
https://mega.nz/#!odoBBKzS!L0PpIYGPS...5mLHDwUL2Facus (this is the first time I have used Mega for sharing files so please let me know if there are any issues).