An electric and thermal model of the hybrid device consisting of a dye-sensitized solar cell (DSSC) and a thermoelectric generator (TEG) is studied for exploiting the solar full spectrum. Analytical expressions for the power outputs and efficiencies of the DSSC, TEG and hybrid device are derived. Temperature-dependent coefficients of the DSSC are introduced and their values being consistent with the experimental data are determined. The effects of the operating electric current, working temperature and temperature-dependent coefficient in the DSSC on the performance of the hybrid device are discussed in detail. The optimum performance characteristics of the hybrid derive at different temperature conditions and the DSSC at the reference temperature condition are compared. The parametric design criteria of the optimal coupling are given. These results obtained here may provide some guidance for the optimum design of practical hybrid devices.