If someone uses a CPAP or home oxygen. These machines need steady power, and a night without apnea support or oxygen is not something to gamble on. A battery power station sized to the device is the real fix — set it up and test it before you ever need it. Many CPAP users can get through one night by sleeping propped up, but check with your doctor first, and if someone is on home oxygen, call your supplier now about backup tanks.
If someone depends on insulin. Insulin lives in the fridge, but it doesn't go bad the instant the power dies. Most types stay usable at room temperature for a stretch — often around 28 days — so don't panic, and don't pack it against ice, which can freeze and ruin it. Keep it in the warm part of a cooler, and call your pharmacy or the manufacturer's line if you're unsure about your specific insulin.
If you have a baby or young kids. Formula-fed babies need clean water for bottles, so boil and cool tap water if there is any advisory, and warm bottles in a bowl of hot water rather than guessing. Little kids lose and gain heat faster than adults — layer them up in the cold, keep them shaded and sipping water in the heat. A familiar toy and a flashlight go a long way; calm parents make calm kids.
If an older adult lives with you. Older bodies handle temperature swings poorly and can get into trouble before they think to mention it. Check on them often, dress them for the room's real temperature, and make sure they keep drinking water. If they take medications that affect heat or hydration, an outage is a good reason to move them somewhere climate-controlled sooner rather than later.