An elderly woman died yesterday after she tried to use her stove to warm her Lower East Side apartment and inadvertently set herself on fire. Widow Claudette Rivera, 72, allegedly turned to her stove for warmth because her second-floor apartment on Ludlow St. had no heat or hot water. Neighbors heard her screams and tried to help her as her clothes caught fire, flames engulfed her body, and smoke filled the hallways. Firefighters were able to put the fire out quickly, and no one else was injured. Adrian Cutner, 65, who was her neighbor for over 30 years, called Rivera a "very, very nice lady," and told the News, "She went up like a candle...It's a classic New York story."