The coupled thermoelstic vibration response of the axially flying viscoelastic sandwich beam was investigated. Considering the interaction of the material deformation and the heat conduction, the coupled governing equations of the axially moving viscoelastic sandwich beam were derived. The exciting load, which consists of temperature function and external excitation force, of the equations was interpolated by a quadratic polynomial of time, then the vibration equation was solved by the method of Galerkin, and the displacement was obtained in every small time by using the numerical method of iteration and convergence to solve heat conduction equation, thus the temperature was gained. The influence of the axially moving speed and thermal loading duration on the response of the structures was studied by using numerical method. The results show that the influence of flying speed on the beam’s displacement is obvious, but on the temperature is small when the beam vibrates stably; thermal impact has a large influence on the beam’s response, and changes the vibration characteristics.