NOAA is a great resource but we need to consider where the corals that end up in our tanks are collected. CJ's article is one I consider excellent because he is looking at our hobby, not the coral reefs in general. Some are cold, cool, warm and many are very hot.
A little excerpt from the articles...
Last, I've included data for the Palau station in the Coral Triangle, a hotspot of biodiversity for corals, reef fish, reef invertebrates, and many other organisms. This area, in keeping with most of the Coral Triangle and the Western Pacific Warm Pool is warm, warm, and warm (Figure 4). The summers are typically in the mid 80's and temperatures drop all the way down to the low to mid 80's in winter"¦brrrr. There is clear seasonality even in Palau, though temperature doesn't vary that much seasonally. Many corals, fish, and invertebrates we might keep in our tanks are collected in areas with a climate like that of Palau.
Though corals may survive, grow and do well in cooler areas, look at where the most diversity comes from. Most of us learned that we had to keep our tanks cool, but that may not be the best thing we can do. There are several people who studied this closely as scientists and are also hobbyists, (not people writing books to sell or considering their next paid lecture,) who questioned the cool water advice long ago and have shown it is not a good advice. Yet the myth of cooler water persists, probably because it is still written in books and suggested by online vendors.
I would never advise anyone to keep their tanks in the upper 80's but I also wouldn't advise keeping them in upper 70's either, unless they kept creatures that require that cooler water for health. Traditionally our tanks have had a daily variation in temp from our lights, this is a good thing, it allows the corals to be accustomed to daily temp variations, just like they have seen for eons. If we lose that daily swing or intentionally try to prevent it then the corals lose that adaptability to variation. They will happily exist in a set temp but invariably something will happen to change that, heater malfunction, electrical outage, etc. and the temp will change, and the corals will stress.