Often when the electricity goes out, the hot water doesn't. Hot water bottles or even ziploc bags filled with hot water and wrapped in a towel will keep chicks warm and can be replaced as needed.
A group of chicks (3 - 4 or more depending on size) will usually generate enough body heat to keep themselves warm if placed in a small, insulated container. I keep several sizes of "picnic coolers" on hand for this purpose, and place a doubled cloth over the top edge to keep the lid from closing tightly.
Chicks can be kept warm enough by your body heat to stay alive, if you can stash them safely close to your skin.
If eggs are in the incubator when the electricity goes out, DON'T TOUCH IT. Cover the incubator with towels or a blanket to retain heat and leave it alone. It will take 2 - 5 hours for it to lose enough heat to damage the eggs (depending on ambient temperature) if you don't lift the lid. If the power isn't back on by then, there are a few other things you can try. A good thermometer is essential - getting eggs too hot is as bad as too cold. The correct temperature is 99 - 100 degrees, and even 97 - 98 degrees will keep them alive for a while. Hopefully there's a thermometer in the incubator that you can use to monitor the temperature without lifting the lid, so you'll know when it drops too low.
If your stove/oven are gas and still operating, you can heat water as described above for chicks and nestle the eggs in hot water bottles or bags. Monitor temperature closely. You can also heat bricks in the oven and use them, wrapped in cloth, to keep eggs warm. Two pans of sand, alternated between a 100 deg. oven and the eggs, may also serve. Keep wet washcloths near (but not touching) the eggs to keep the humidity up.
If you must travel or leave the house, eggs nestled in 100 deg. sand (or those rice/corn packs) that has been poured into a pre-warmed picnic cooler and then covered with a couple of towels will stay warm for several hours with the lid shut. In this case the eggs don't really need to "breathe" so you can let the lid seal. (Eggs do exchange oxygen with their environment, but not rapidly enough to worry about for the time span they'll stay warm without being disturbed.)
If none of your appliances are working and there's no hot water left, any means of warming sand/bricks/rocks/bags of uncooked rice, etc. are worth a try - the sun, candles or any open flame, etc. I'd be careful using the warming devices made for people's feet, hands, etc. - I think they get too hot initially to use for eggs, but they can be used for chicks if wrapped in a towel - chicks will move away if they get too hot; just make sure the chicks have the space to do so if necessary.
Also, if you have chicks AND eggs, don't forget that chick body temperatures are just as suitable for incubating eggs as adults, and the majority of eggs survive older siblings in the nestbox. Put the eggs in under the chicks. Oddly enough, eggs retain heat fairly well and will also help keep the chicks warm. (If you have infertile eggs stashed around like I usually do, or even grocery store chicken eggs, these can be warmed and placed with chicks to help them maintain a stable temperature.) Of course there is some risk that an egg will be damaged, but no eggs will survive if they are chilled.
Most of all, don't give up. Our electricity was out for a solid week last year after a thunderstorm took out a tree and tore our power line down, and all of our chicks and about 70% of the eggs made it through. Most of the eggs we lost were eggs that were under birds in nestboxes, so if I had to go through it again I'd pull the eggs, replacing them with infertile "spares," and try to keep them going myself until the power was back on and the birds returned to their normal routine.
As always, just my experience.
Heike Ewing, Bear's Den Aviary / "BearsDen" on IRC
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