Non-extremal black holes, which emit thermal Hawking radiation, have two horizons: the event horizon or outer horizon and the Cauchy horizon or inner horizon. Surprisingly, for a broad class of solutions to the Einstein equations, the product of the areas of the inner and outer horizons is the square of the area of the horizon of the zero temperature black hole obtained from taking the smooth extremal limit. We use the attractor mechanism in supergravity to motivate this result and offer a CFT interpretation.