The short answer
During a power cut, insulate the tank to hold its heat, keep the filter media wet, and run a battery-powered air pump for oxygen. A tank cools slowly, so heat is rarely the first problem — the bigger risks are the filter stalling and oxygen dropping. Wrap the tank, keep the water moving if you can, and avoid feeding until power returns.
Hold the heat in
Water loses heat slowly, especially in a larger tank, so your job is to slow that loss further. Wrap the aquarium in blankets, towels or foam boards, including the sides and back, and close the lid to trap warmth. Keep the room warm however you can and shut the curtains. A few degrees’ gentle drop over several hours won’t harm most fish — what stresses them is a fast plunge, so insulation buys valuable time. Monitor with a thermometer if you have one.
Keep oxygen and bacteria alive
With the filter off, two things degrade: oxygen drops and the beneficial bacteria in the filter start to suffer. Tackle oxygen with a battery-operated air pump and air stone — a cheap one is worth keeping for exactly this. No pump? Gently scoop and pour tank water with a cup every so often to break the surface. Meanwhile, keep the filter media submerged and wet so the bacteria survive; if the outage is long, give the media a quick swish in tank water before you restart, so nothing stagnant washes into the tank. See what to do during a power cut.
When power returns
Restart equipment and check the filter runs clear before it flows back into the tank. Bring the temperature back up slowly with the heater rather than forcing it, and hold off feeding for a day so waste doesn’t build while the biology recovers. Test the water over the next few days in case the pause dented the cycle — a test kit will show any ammonia or nitrite. Keeping a battery air pump on hand is the single best bit of outage insurance.