Electromagnetic dampers (EMD) have been widely studied and designed in the control of vibrating structures. Yet, their use for space applications has been almost negligible, due mainly to their high ratio of system mass over damping force produced. The development of shunted circuits, and in particular negative impedances, has allowed higher currents to flow in the device, thus obtaining an increased damping performance. However, the need for a thermal analysis has become crucial in order to evaluate the power and temperature limits of EMDs, and hence allow a more efficient optimization of the whole device. This paper presents a multiphysics Finite Element Analysis (FEA) of an EMD in which the thermal domain is integrated with the electromagnetic and mechanical domains. The influence of the temperature on the device parameters and overall performance in the operative temperature and frequency range of a space mission is shown. It follows a design optimization of an electromagnetic shunted damper for 5-kg SDOF to obtain a second-order filter. In particular, the analytical results are compared with the typical transfer function of a viscoelastic material. This paper demonstrates the feasibility to achieve the same slope of -40 dB/dec while considerably decreasing the magnitude of the characteristic resonance peak of viscoelastic materials.