If you are comfortable with doing mechanical work yourself, an auxiliary ATF cooler is not difficult to install. Finding a good safe place to mount it is probably the most important thing. I don't know if Volvo sells them; I have a manual transmission car.

Heat kills automatics. They are plenty strong enough otherwise.

Yes, Volvo sells the wiring harness. A bit pricey at $100, but it comes with instructions and you simply need to find the existing receptacle in the area of the rear electronic module to connect it to. Don't worry about the fuses that may come in the package. Software is not required. There's considerable confusion between European and North American trailer lighting systems, e.g. combined brake/signal lights vs. separate amber lights, rear fog lights required on EU trailers, and no electric brakes in Europe).

The Volvo kit will come with hardware that will allow you to mount the flat plug outside the car on a Volvo trailer hitch receiver. I didn't bother with that; I taped up the wires, and run the plug out under the trunk lid when I need it.