Purpose <p>Since single-walled carbon nanotubes (SWCNTs) possess excellent electrical, thermal, and mechanical properties, they have attracted significant interest from researchers. However, the temperature sensitivity of SWCNTs’ mechanical properties has been overlooked, and their nonlinear temperature-dependent vibrations have received little attention. Additionally, for an SWCNT in nanoelectromechanical systems (NEMS), the nonstationary resonance may be induced by the slow changes in the load’s frequency and amplitude during the initial or final stages of vibrations.</p> Methods <p>This paper explores the nonlinear nonstationary vibrations of SWCNTs using a temperature-dependent nonlocal nonlinear Bernoulli-Euler beam theory. First, the nonlinear partial differential equation is discretized into a nonlinear ordinary differential equation using the Galerkin method with the first-order bending mode. Subsequently, the perturbation equations for nonstationary oscillations and the approximate analytical solution for the primary resonances are obtained by the method of multiple scales.</p> Results <p>Key findings from the approximate solution and the perturbation equations include: (1) Thermal stress weakens the SWCNT’s stiffness and significantly influences both primary resonances and nonstationary vibrations. (2) Slow variations in load frequency and amplitude remove the multivaluedness of the curves of amplitude response, eliminating the jump phenomena of vibration amplitudes. (3) Response curves with slow variations in load’s amplitude and frequency are closer to the curves of primary resonances than those with rapid variations.</p> Conclusion <p>The slow change with time of load frequency and amplitude significantly affect the nonlinear vibrations of SWCNTs.</p>