1. An apparatus comprising: an array of non-volatile storage elements; a heating element configured to heat a first set of the non-volatile storage elements to anneal the first set of non-volatile storage elements; and a heat shield configured to mitigate heating for a second set of the non-volatile storage elements 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, wherein the heat shield comprises an active cooling device configured to be in an activated state during annealing of the first set of non-volatile storage elements to transfer heat away from the second set of non-volatile storage elements.