In this work, a smart composite structure with damping and stiffness control ability is proposed. The multilayered arrangement has a shape memory core, whose damping and stiffness are tuned by temperature control. The structure is divided in several zones, each of them can be heated in real time using temperature regulation to reach the expected mechanical properties provided by the strong temperature and frequency dependency of the stiffness and loss factor of the viscoelastic core. The heat flux, which is used to tune the mechanical properties, is provided by copper tracks printed on an electronic board used as skin of the sandwich. The paper presents a model-based design process, including thermal and mechanical simulations, providing the gradient temperature fields which are required to obtain a specific damping and stiffness. Experimental tests are finally presented, considering three configurations with various temperature sets corresponding to three different compromises between static stiffness and dynamic damping.