Inverse temperature dependences of the detwinning stress of face-centered cubic deformation twins were discovered by studying the effect of elevated temperatures on plastic deformation properties of multilayer twin/matrix structure of the Cu-8at.%Al alloy. The critical stress of detwinning was found to increase remarkably with temperature when plastic yielding of the twin/matrix structure occurred by the π detwinning mode. However, when the alternative π/3 mode of detwinning was involved, a decrease of the detwinning stress with an increase of temperature was observed, instead. Thus, the twin/matrix structure behaved in two opposite ways, showing anneal hardening (the case of π mode) or anneal softening (the case of π/3 mode) upon temperature increase. As concluded, the dual effect of temperature on the detwinning stress resulted from irreversible reduction of internal stresses pre-existing within the deformation twins. The complete reduction of the internal stresses at about 530°C led to the equivalence of the critical stresses of different detwinning modes and a large decrease of the yield stress anisotropy of the twin/matrix structure. It was postulated that temperature induced annihilation of the internal stresses resulted from constriction of extended cube dislocations pre-existing within deformation twins. The temperature limit of about 540°C, beyond which the twin/matrix structure became unstable due to recrystallization, was also established. Moreover, transfer of plastic shear throughout the twin/matrix structure was found to be predominantly controlled by internal dislocation substructure of deformation twins, not by the twin/matrix interfaces.