While I'm in total agreement with Ron regarding the ideal temp for reef tanks, the "Q10" metabolic model he's using to justify this statement is only roughly valid for some species of corals. Many (Echinopora is one I can think of off the top of my head) maintain temperature independent metabolic rates over their range of acclimatization.
Lots of people justify keeping their temperatures low by citing the difference in dissolved oxygen or respiration as temperature increases. When someone tells you that, it's obvious that they haven't crunched the numbers. The differences are extremely small. The difference in saturation between 76 and 86 is about 7%. Even taking into account the effect on respiration (again, assuming the Q10 model, which is an overestimate in most cases), in the event of an emergency, temps at the lower end grant you a few seconds to a few minutes of extra time before oxygen is limiting- not hours.
To give you an example of the impact temperature has on oxygen, imagine you had a 65 gallon tank that had nothing in it but a single, medium-sized clownfish. If you consider only the direct impact of temperature on dissolved oxygen, that tank can support the clownfish for a bit over a minute and a half longer in the event of a power outage if it was at 78 than at 86. If you also assume that the clownfish follows the Q10 temperature dependence model (which my works suggests isn't the case) then you get about 5 extra minutes to solve the problem before the fish starts suffering from low oxygen. That's unrealisticly low stocking though, and doesn't include respiration from LR or LS. When you include more fish or LR and LS those times would be reduced dramatically.
That line of reasoning is probably the #1 reason people run their tanks cooler than normal, but the presumption is wrong. Neither of these situations is worse than the other. The thermal stress threshold in reef animals is set by acclimatization, not genetics. The rule of thumb is that stress begins at 2-4 degrees above the average maximum seasonal temperature. Whether that seasonal maximum is 78 or 82 is immaterial. The margin of error is still the same. There are absolute genetic limits to what corals can be acclimatized to, but for most corals those aren't hit until temps in the 90s.