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The thermoforming of thermoplastic sandwich structures based on the same matrix polymer for the face sheets and the core requires precise temperature control both before and during forming. Two opposing requirements must be satisfied: the face sheets must be heated to above the glass transition temperature Tg of the polymer whereas the temperature of the core should not approach Tg in order to avoid the collapse of the foam cells. A numerical model was used to determine the optimal thermal parameters for thermoforming using an inverse method.