First and foremost - don't panic! Most aquarium inhabitants can happily survive the slightly lower temperatures of a heated room for a limited time, so temperature is not a huge concern and can be boosted by adding sealed bottles of hot water if necessary. More critical is the water quality, as without filtration and water movement, these are the factors most likely to cause problems. Turn off the filter, as without oxygenated water flowing through the biological media, harmful toxins can build up that are discharged into the aquarium when the power is restored. If the power is out for an hour or more, remove some filter media and store it in a bucket with a little water from the aquarium to keep it moist as the bacteria will survive better out of water with exposure to atmospheric air. As the temperature will fall, cover the aquarium with a duvet, blanket or towel to slow heat loss and keep the fishes calm. However tempted you may be, never feed the fish if the filtration isn't working.
A real life-saving emergency piece of kit can be assembled using a battery operated air pump and a chemical filter such as Polyfilter, which will remove ammonia and nitrite thanks to the action of special resins. Other media such as zeolite, or even mature bio filter media can be added to an air-operated box filter. In the case of marine tanks, a battery operated air pump will ensure water movement around liverock, which will maintain water quality. In the absence of a better option, syphoning water from the tank and pouring it back in can help maintain oxygen levels if performed as needed.
The most important aspect of any loss of life-support equipment is the effect on water quality once feeding is resumed. I would recommend adding a filter bacteria starter to aid recovery and keep feeding to a minimum until both ammonia and nitrite levels are seen to be under control through regular testing. Be prepared to carry out a series of water changes in the days after a power loss and treat your tank as if it were the unstable system it was in the early days of maturation.