Shape memory polymers (SMPs) can remember two or more distinct shapes, and thus can have a lot of potential applications. This paper presents combined experimental and theoretical studies on the wrinkling of single-crystal Si ribbons on SMPs and the temperature dependent evolution. Using the shape memory effect of heat responsive SMPs, this study provides a method to build wavy forms of single-crystal silicon thin films on top of SMP substrates. Silicon ribbons obtained from a Si-on-insulator (SOI) wafer are released and transferred onto the surface of programmed SMPs. Then such bilayer systems are recovered at different temperatures, yielding well-defined, wavy profiles of Si ribbons. The wavy profiles are shown to evolve with time, and the evolution behavior strongly depends on the recovery temperature. At relatively low recovery temperatures, both wrinkle wavelength and amplitude increase with time as evolution progresses. Finite element analysis (FEA) accounting for the thermomechanical behavior of SMPs is conducted to study the wrinkling of Si ribbons on SMPs, which shows good agreement with experiment. Merging of wrinkles is observed in FEA, which could explain the increase of wrinkle wavelength observed in the experiment. This study can have important implications for smart stretchable electronics, wrinkling mechanics, stimuli-responsive surface engineering, and advanced manufacturing.