Can anyone identify the story within the play "Love From A Stranger?"

actorconsultant

I need help. I am preparing to direct a production of "Love From A Stranger" (adapted from a short story by Christie) and I would very much like to understand a particular reference in the play. Near the end of the play the character Bruce says, "I know where you got the story from. I've read the book myself." The story in question involves a woman who kills her sick husband by opening the window of his sick room and chilling him to death. Later, she uses hot water bottles in the bed to make it seem he was at a normal temperature when he died. Can anyone tell me what story is being referred to? Is it a reference to a Christie book? Could it possibly be one of the "1001 Tales of the Arabian Nights," which is also referenced in the play? Roughly the same story is told in the film "Double Indemnity." Is it possibly a true crime story on which both works are based?