A first-of-its-kind design methodology to realize origami-inspired multi-layer frequency selective surfaces (FSS) with a thermally actuated smart shape-shifting spacer layer is presented. The spacer not only features low dielectric losses but can also change its shape to maintain optimum inter-layer distances as the Miura-FSS structure is folded to preserve desired frequency response. It also introduces unprecedented high mechanical strength making it suitable for wide range of applications. The proposed structure features twice as broad bandwidth as compared to single layer Miura-FSS and an excellent angle of incidence rejection.