It all depends on the corals you have. Some corals come from deep water (e.g. deepwater acros) and other corals are used to shallow lagoons (e.g. gorgonians) and then there is everything in between.
Lagoons can get quite warm at 81-84 degrees while deep water can get into the low 70s and colder.
And then there is also seasonal variability
Winter months (approx. December-March): 78-80 degrees F. / 25-26 degrees C.
Summer months (approx. April-November): 81- 84 degrees F. / 27-29 degrees C.
What this means for us with corals in our tanks?
Most people keep tanks between 78-81 degrees w/o issue. Luckily some corals are tolerant of temperature ranges and can acclimate to a variety of water temperatures (within reason). And if you had picked up a frag from a coral that is already living healthily in an aquarium, then most likely you shouldn't have any issue with it in the 78-81 range. One thing to note though, anything above 82 degrees is pushing the limits of heat tolerance for some corals and you are risking a bleaching event.
I've been lucky enough to dive in 8 different locations in the tropics (Pacific, Caribbean, FL Keys) and with every location the surface of the water is nice and warm (~80 degrees) and when diving at deeper ~60-75 feet, the water is noticeably cooler dropping into the low 70s and all along the way I saw different species of corals.
So, if you are really concerned about temperature, do more research on the coral you have in your tank and find out what it's preferred temp ranges are.
Alternatively, temperatures between 78-81 degrees should be fine.
Avoid temperature swings in a 24 hour period. Consistency of temperature goes a long way in keep corals alive.