I lived in Manhattan in a bunch of different apartments and frankly, I don't know if I could have heated any of them if the "heat" had been out for an extended period. Something not too uncommon but generally an isolated problem, is having a boiler go out for a while in an apartment building. The electricity and gas will still be on and people will resort to all kinds of scary means to keep warm, like running the oven with the door open or using the burners for heat. Some try heating pots of water and then putting them in other rooms to try and warm them up. Some people develop elaborate systems of opening and closing doors in sequence to move heated air to different rooms in the apartment. Of course, hot plates and other electrical items often get overused and overloaded, too.

Many of these apartments are old, not insulated, the doors and windows are drafty, very little sunlight enters, no fireplace--it's not a great situation to be in. Without putting yourself and your neighbors in danger by actually burning something inside your apartment, trying to seal off a room and hunkering down with lots of blankets and such is probably the best you can do when all the utilities are out. Candles might warm your hands, but that's about it.