Three-dimensional coil structures assembled by mechanically guided compressive buckling have shown potential in enabling efficient thermal impedance matching of thermoelectric devices at a small characteristic scale, which increases the efficiency of power conversion, and has the potential to supply electric power to flexible bio-integrated devices. The unconventional heat dissipation behavior at the side surfaces of the thin-film coil, which serves as a “heat pump,” is strongly dependent on the geometry and the material of the encapsulating dissipation layer (e.g., polyimide). The low heat transfer coefficient of the encapsulation layer, which may damp the heat transfer for a conventional thermoelectric device, usually limits the heat transfer efficiency. However, the unconventional geometry of the coil can take advantage of the low heat transfer coefficient to increase its hot-to-cold temperature difference, and this requires further thermal analysis of the coil in order to improve its power conversion efficiency. Another challenge for the coil is that the active thin-film thermoelectric materials employed (e.g., heavily doped Silicon) are usually very brittle, with the fracture strain less than 0.1% in general while the overall device may undergo large deformation (e.g., stretched 100%). Mechanical analysis is therefore necessary to avoid failure/fracture of the thermoelectric material. In this work, we study the effect of coil geometry on both thermal and mechanical behaviors by using numerical and analytical approaches, and optimize the coil geometry to improve the device performance, and to guide its design for future applications.