<p>Studying the methodology for changing energy-damping factors and thermal quality in vibrating nanobeam resonators is important, and the main goal of this work is to study the thermal quality factor of the constructed model. An analytical thermal model has been developed in this study to investigate the effects of varying thermal and mechanical relaxation durations, influenced by Young’s modulus, on viscothermoelastic nano resonators of fractional order. It was formulated using a hyperbolic two-temperature dual-phase-lag heat conduction model. The thermal quality factor has been calculated and analyzed using three distinct models of heat conduction: one-temperature, two-temperature, and hyperbolic two-temperature models. This study aims to assess the influence of the fractional order parameter of Young’s modulus, length scale, two-temperature parameter, and mechanical relaxation time parameter. The model has been used on a silicon-based nano-resonator. All examined parameters may be adjusted to significantly enhance thermal quality characteristics.</p>