Oh wow! My Kawasaki Concours I used to have had a section in the manual warning to never let the engine idle for more than 10 or 15 (don't recall which) without shutting it down to let it cool off, but I haven't seen any similar warnings for the CTX.
One of the things that bugs me about the CTX is that it doesn't appear to have a real temperature gauge. Instead, it looks like it's the same as the dummy lights in disguise on most cars today where it reads cold, then "normal", then hot with no real in-between. A proper gauge could have given a bit more warning that things were starting to get too hot.