I had a similar problem on my car and it turned out to be one of the keepers or U-pins wasnt fully seated inside the engine bay allowing the cable to slip out of place when trying to shift.

I have a 97 Dodge Avenger 2.0 DOHC N/T FWD with the F5MC1 trans and 420A motor. Shortly after I bought it (it had roughly 111k miles on it when I bought it) I had to replace the clutch then the trans itself went. I bought a used trans from a junkyard and had it professionally checked and...

Is your car actually overheating? Are you losing fluid at all? My Avenger was constantly overheating and it turned out to be just a bad radiator cap. Never had a radiator cap go bad until then on any car Ive owned but glad it was a simple fix.