The influence of the coupling between strain rate and temperature becomes domineering in the nanoscale beam. In this work, the free vibration of nanoscale beam resonators is analysed using Green and Naghdi's theorem under the two-temperature model (2TGNIII). The influence of two-temperature parameters in a nanoscale beam is studied for beams under simply supported conditions. Exact expressions for frequency shift and the thermoelastic damping have been derived in the resonator, and calculation outcomes have been presented graphically with respect to frequency shift, natural frequency, and thermoelastic damping. The scale of length and thickness for a nanobeam equal to 15*10^-9 m and equal to 1.3*10^-12 s for time.