To be honest, I wouldn't worry about 120F. Until I got my ATF temperature gauge installed last year, I had no clue what my transmission temperatures were for any given condition. Most people don't. Where I live, it is common for winter ambient temperatures to be -20C/-4F, and can reach -40 at times. There are many cities throughout Canada and northern Europe that experience similar cold temperature extremes. And plenty of vehicles driven in those cities (and they have been driven in those conditions for just as long as cars have been driven anywhere else).
With the addition of the gauge, in early winter/late fall, and ambient temperatures only slightly below freezing, I have done many trips where the temp never goes above 100F. There is currently no auxilliary cooler on my vehicle.
Yesterday, after parking outside only a few hours in -18C/0F, the gauge started off at only 11F. Granted, I sat inside waiting about 5 to 10 minutes waiting for my wife while idling before driving, and it slowly crept up to 60F, before we drove off.
My point is, I have never heard of a transmission failure due to the cold in any of the northern cities. I do not think you can realistically overcool an automatic transmission, at least from a longevity perspective, unless you get down to temperatures for an extended period where the fluid is far too viscous to flow properly. Gaining heat very quickly from the radiator, I don't think that's an issue.
If real winter is a concern for you, then either install a tranny cooler with a built-in cold bypass, or add a cold bypass valve to one without it. From the get go, I've found the former to be the cheaper option as the bypass valves separately add a lot to the overall cooler price. Santa was good to me, and brought me a B&M (one of the Dana made brands of coolers) for Christmas. I just haven't been in a rush to install it over winter (not needed this time of year, and too cold in my unheated garage to work comfortably, unless it's work I absolutely need to do).
