The correct answer is B) opening dead spaces to check for heat or fire. When overhauling a fire in the living quarters, it is crucial to thoroughly inspect all areas, including dead spaces, to ensure the fire has been completely extinguished. This is a crucial step to prevent the fire from reigniting or spreading. The other options are not directly related to the proper procedures for overhauling a fire in the living quarters. A) operating the emergency generator is not necessary for the fire overhauling process. C) sounding the "all clear" signal should only be done after the fire has been fully extinguished and the area is deemed safe. D) evacuating the vessel would only be necessary if the fire was still actively burning and posing a threat to the crew.