Most aquarists with reef tanks understand that maintaining their corals within the proper temperature range is important in order to keep them healthy and growing. If the temperature is too low or too high, the zooxanthellae algae, which most corals require for survival, will die or vacate the polyps. When the algae leaves the coral, it exposes the white base calcium carbonate of the coral, it is sometimes called Coral Bleaching. You may recall the news stories about coral bleaching in some of the world's coral reefs, which reportedly began in the early '90's.
So, what is the proper temperature to keep your reef tank at? Many LFS keep their tanks at 75-78°F and recommend to their customers that they do also. A number of OLS coral shippers recommend keeping your tank temperature at 82°F.
With so many recommended temperatures, what is the best temperature for your reef tank? Perhaps the best way to make a decision is to look at what the temperatures were when your corals were in the wild. If you look at Coral Reef Regions in the World, you will see where corals grow in the wild. If you compare this to the indicated temperatures in NOAA's Sea Surface Temperatures, you will see that a vast majority of coral reefs are found where water temperatures are between 80°F and 89°F.
Perhaps a more pertinent reef tank temperature question, particularly during the summer months, is "how high is too high"? When do you really need to crank up that electron sucking chiller you paid a half a month's wages for?
The first place to start is to determine where your corals originally came from. The Indo Pacific, Caribbean and Red Sea are where most of the corals in the aquarium trade are collected. Perhaps the easiest way to find out is to ask the LFS or OLS where you purchased your corals where the corals were shipped from.
Since most aquarium corals are collected from the Indo Pacific and the Caribbean where the water temperatures are routinely between 85 and 89 degrees Fahrenheit, perhaps you may not need to get too concerned as long as your tank temps do not rise above this level.