Apparatuses, systems, methods, and computer program products are disclosed for preventing overheating, for annealing non-volatile memory. An apparatus may include an array of non-volatile storage elements. A heating element may be configured to heat a first set of the non-volatile storage elements to anneal the first set of non-volatile storage elements. A heat shield or cooling element may be configured to prevent a second set of the non-volatile storage elements from overheating during annealing of the first set of non-volatile storage elements, to mitigate data errors for data stored on the second set of non-volatile storage elements.