For my tanks (this was in southern Florida), I had fans built into the canopies that ran only when the lights were on. This served to blow off some of the heat produced by the lights, so it didn't get the chance to heat up the water as much.
However, I don't think 81 is too high. As with a lot of aquarium parameters, I think its sudden changes that stress our aquarium fish/inverts. My tanks ran mid-80s in the summer months with no problems or die-off of coral, sponge, or fish.
Look into the data of the temperatures of tropical reefs in the wild. Those I dove had temps at the bottom (80ft or so for where I lived) that stayed 78-82 in the summer months. The shallower were even hotter, topping at 85ish.