Personally, I would remove all batteries and store them away from high heat (the same is probably true for extreme cold as well). If they are packed inside a box there is no ventilation and they will just heat up and cook themselves based on the ambient temperature of the storage area. A dark cool closet is best. In some cases I have actually removed the logic-boards and stored them in static bags in a cool location as they are smaller and take up less space than the case itself. cCassic Analogue boards are actually the most susceptible to heat, but also more complicated to remove from the case and store like that, although not a bad idea either and think I will!