I vaguely remember reading an article that claimed without the sunlight ,the surface temperature of the Earth would soon fall to an average -40 F. Supposedly the heat of the core leaking out would keep it that “warm” for a long time. -40F would be cold enough to freeze all water including the oceans ;I suppose some sort of life might cling precariously to the temperate zone around active volcanos.
Another science fiction story of the 1950? had the survivors scooping buckets of frozen oxygen from the bitter outside and leaving them to melt by the fireside.The science often gets swept aside by artistic license.