There is an oxygen component as well though to temperature. High temperatures = higher respiration = higher oxgyen use. The oxygen levels in our tank though are no where near as high as the ocean. Therefore, increasing the respiration rate in an already oxgyen low enviroment CAN be stressfull on inhabtitants, even though the temperature itself is not. This leads to the aquarist wanting to control their temperature and keeping it on the lower end, so I personally certainly do see a good reason for controlling temperature fluctuations over 80-81.
There's a lot of truth to this, but also a lot of common misconceptions and oversimplifications.
There's certainly an oxygen component to be concerned with for a few reasons. One being that warmer water holds less oxygen at saturation. However, over the range of temps we're talking about in reef tanks the difference is negligible. There's something like 6% difference going from 78-86. You have to go above 90 before the saturation point even drops below 200% of the lower safe limit.
Of course the amount of O2 the water
can hold is a different story than what it actually
does hold. Adey has shown that during the day the water column on the reef is often hyperoxic and then becomes hypoxic at night. The differences are even more pronounced within coral colonies and the reef structure itself. He also found that O2 in a captive reef very closely resembles that seen in nature. Eric Borneman has done some work testing more tanks with similar results. I've only taken a few readings in tanks that resemble what you see in the hobby and they were all replicate tanks, but my readings didn't suggest that oxygen was any more limited than in nature either. In some tanks very heavily stocked with fish, oxygen availability may be an issue, but in the average reef tank it doesn't seem to be.
Of course the demand for O2 does generally increase with temperature. The rule of thumb for poikilotherms is that for every 10 degree C increase, metabolism will double. Over the range of reef temps that ends up being, very roughly, 9% increase in metabolism per degree Fahrenheit increase in temp (the trend isn't actually linear, so this just gives a rough estimate). However, that rule of thumb doesn't actually represent reality. As it turns out the amount of increase actually depends on the thermal history of the animal. At a given temperature, lets say 80, an animal that normally sees an average temp of 82 actually uses less energy than an animal of the same species that normally sees a temperature of 78. As temperature continues to increase the metabolism of the individual from the colder environment increases faster than the one from the warmer.
Thermal history also sets where the stress threshold for the animals is. Lots of people keep their tanks cooler than the natural average due to the mistaken belief that the danger threshold is a set value and lowering their temp will give them more room before they reach it. That isn't the case. The stress threshold is a product of acclimation, so lowering the temperature only acts to lower the threshold as well.
