The very short version is that most (i.e., not all, only most) coral reefs have historically experienced temperatures in the neighborhood of ~78-84 F and have spent relatively little time outside this range. Some reefs are hotter than typical and regularly spend time in the 84-87 F range (and even higher in the Persian gulf) and some reefs are cooler and regularly drop down to the upper 60's, or even lower. However, the extremes are poorly tolerated by most corals. Corals from all reefs can thrive at temperatures in the neighborhood of 77-82 F, and most are flexible enough that they can tolerate a few degrees higher or lower for a bit. You can see much more detailed discussion in the series.
Back to the original question: if it were my tank, I'd use a fan on it as suggested. I think a temp of 83 F is fine and pretty much all our critters will thrive at that temperature, but I wouldn't want to intentially let it get much higher. Some corals will tolerate many degrees warmer without problems, whereas those form cooler reefs won't. Putting a fan on should allow better temperature control.
As a side note, greenbean is hecka smart and has given oodles of great advice; I'm a Ph.D. candidate in oceanography here at UH, working on coral eco-physiology; I live about 3/4 of a mile from the nearest reef and work adjacent to one; the temperature there averaged about 82 F today, which is a degree or two F lower than normal for this time of year (and 6-8 F warmer than is normal for 6 months from now, but then our reefs are on the cool side here in HI).
cj