I had a similar chart waaaayyy back when I was in school. The 20 minute failure was at above 300* as I recall. However, there have been 6 generations of trans fluid since then. For example Dexron VI for GM and similar for Mercron and Mopar. With today's fluids, I wouldn't even install an additional external cooler unless I saw consistent and regular temps above 220*. A once in a while spike while towing, is nothing to worry about. And the "idiot" gauges have nothing to do with anything anymore. All the modern vehicles will intervene and prevent sudden temp spikes with trans shifts and high speed fan activation, and if you ignore things, they go into limp mode to protect themselves.
That being said, you won't hurt anything with an additional cooler, unless you live in the far, far north (arctic). Overcooling (for the vast majority of us) is as much a myth as is "250* is too hot and damage is being done". Modern trans fluids are quite remarkable.
"If the women don't find you handsome, they should at least find you handy." - Red Green