I used to tow with BA ute it ran very hot and would overheat on hot days, put an oil cooler on and no problems.

Then got a BF it did not run hot, But i put the cooler on anyway, Does not cost much, and is cheaper than fixing a cooked motor or tranny.

We used to get all servicing and repairs done by a workshop that handled taxis. I suggest you do the same. This was after getting caught with red tranny oil in the radiator of an EL. I had been watching the wife's car any signs but in the end was too late. That was after following the advice of a well known 'all makes' automatic transmission repair service. So much too for my more regular than necessary servicing schedule and tranny fluid replacement.

I suggest you consider a pre-emptive strike by replacing the water radiator ASAP with a larger capacity, better quality aftermarket one. It is the water radiator that has a failure problem.

I wouldn't chance buying a transmission cooler and fitting it in-line myself or with an ordinary garage. Fittings are uncertain in quality and installation. In the engine bay it is hot and there is no air movement. You need someone familiar with hard working Falcons in warm areas.