Agree. This incessant desire to keep temperature change to a minimum is really strange to me. Reefs are places of change - and 8+ degree daily fluctuations are the norm on reef crests.I believe temperature is much less important than internet forums would lead you to believe.
I have a small heater that kicks on around 72-73 degrees, im not sure if it ever needs to actually run. I dont have any real means of cooling the tank or of measuring/recording temperature. If my house is comfortable for me, it's also comfortable for my tank.
I do have a large enough generator to heat/cool the room in case of a power outage, which is the only time temp would deviate far enough to be concerning.
I'd never know my tank hit 81.2 degrees, but assuming all it's inhabitants looked good/not stressed, I wouldn't do anything about it.
I have my heater set to come on at 78 and go off at 81. 81 is a pretty normal temp - you're not anywhere near danger zone. I don't worry about it unless I'm down to about 72 or up around 84.