I also agree the 81.3 is not that bad. But, its the swing that becomes the issue and if he's targeting say 79 degrees and the new lighting has caused an increase to a base temp of 81 than he's still going to need to address this issue when summer rolls around. Now, if he can find a way to keep the swing down than there is nothing wrong with running a reef at 82.
The first time I ever went to atlantis aquarium when they were in freemont, I walked in the door looking at his main sps show tank and the temp display said 86 degrees and the colors were spectacular. I target 80 degrees because I want room for error if I have a mechanical breakdown of my chiller and heater. So if my heater fails halfway though the night and I ran my tank at 78, it would get cold a lot faster. If I ran my tank at 82-83 and my chiller failed, than my tank would meltdown pretty quick.