Wow, I was just about to ask the same question. I don't want to have to get a chiller for the onlytwo months that the temperature gets to right at 80 degrees. So yes, what would be too hot?
well I can tell you what I have read and heard and learned but for sure go check and see what you can find out...
in "most" of the worlds tropical seas the reef water temp will be at or close to 78 "most" of the time. some places like our gulf run warmer in the summer due to our gulf having a lot of shallow sand bed and the shape of the gulf does not allow the colder Atlantic water to mix and cool the gulf as much as say the eastern carib that is more open to the east.
in places like the great barrier reef and the keys they are looking at several things that are thought to be killing coral, one of the things is that they have seen average sea temps rising a couple of degrees.
coral evolved for ages with a range of water temps, they can take a short term temp swing and recover.
but a long term high temp is not good for them, just as we do not want to live and work in 90 deg heat all the time and drop the temp to 80 and we are much more able to cope.
also this has to do with what corals you are keeping, where did they come from ? what are the normal / average temp and salinity in that part of the world ?
if you setup a "gulf only" tank then you could run 80-83 summer day temps for part of the year but you still want to run below 80 for say 8-9 months of the year. our winter gulf also gets really cold compared to a true tropical reef zone. the gulf is not the tropics, close to them but not in them.
so study the corals, fish and other things you want to have and what the long term norms are where they live and use that to guide you.
what I found is that 78 is a very very good number to peg the system at.
78 goal, 76 low ok, 81 high ok but always going back to 78 as much as possible.
also the larger the volume of water the more it will tend to stay at a set temp. small volumes heat and cool faster.