actually, humidity will damage it before heat will, but yes, temperature change (especially rapid temp change) is not good for it at all. It also depends on what kind of acoustic it is (what woods, whether its a solid or ply top, why type of bracing, what body style, ect ect) Go to Guitar Center and in their accessory section they have all kinds of cool little toys for keeping your acoustic nice and safe. But you should still move it.
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