When the power goes back on, it will wake you, so you can check the condition of your foods in the freezer. If freezer foods still have ice crystals then they can be refrozen. Try to determine how long the power has been out. Check the internal temperature of the food in your refrigerator with your quick-response thermometer. A liquid such as milk or juice is easy to check.
Spot check other items like steaks or left-overs also.
If the internal temperature is about 40 degrees, it is best to throw it out. If the food in the freezer is not above 40 degrees and there are still ice crystals, you can refreeze. There will be loss of quality with refreezing, but the food will be safe. If the refrigerator was out for more than 2-4 hours, it would be best to discard the perishables. After a prolonged power outage, it is important to take actions to reduce the chances for a home fire.