Abstract: The on-orbit space structures are subjected to periodic solar radiation, which induces thermal deformation and thermal vibration. Considering the influence of errors in the design, assembly, and manufacturing processes, the study of dynamical response for the on-orbit space structure models with random parameters is of great theoretical significance and practical value. In this paper, a stochastic dynamical analysis method based on the polynomial chaos expansion (PCE) is proposed to study the thermal vibration of flexible multibody systems with multiple random parameters. The influences of different random parameters on the thermal vibration is explored and analyzed. Firstly, in order to derive the spatial thermal structure coupling model, the absolute node coordinate formulation (ANCF) is used to model the spatial simplified model involving thermal effect, and the Fourier temperature element method is used to analyze the structural temperature response. Secondly, the surrogate model of the stochastic dynamical system is constructed through PCE method, and the sample points are selected by the monomial cubature rules (MCR). Then, the PCE coefficients are obtained by the stochastic response surface method (SRSM). The mean and standard deviation of thermal vibration response are obtained, which are compared with Monte Carlo simulation (MCS) results to verify the accuracy and efficiency of the proposed algorithm. It is found that the proposed method meets the accuracy requirements. Especially, compared with the MCS, the sample points of the proposed method reduce to only 1.5% and the calculation efficiency is improved by 76 times. Finally, the influences of several different random parameters, including the elastic modulus, beam length, solar radiation absorption rate, surface radiation coefficient, solar radiation intensity and solar radiation angle, on the thermal vibration response of the structure are studied. The obtained results show that the random dispersion degree of beam length and elastic modulus have the most obvious influence on the thermal vibration response.