<p>Ultra-short pulses have seen rapid development and wide application in the nano-machining of viscoelastic structures. Consequentially, the transient thermo-mechanical responses at the micro/nano scale have gained utmost importance. At the microscale, the significance of size-dependent effect in elastic deformation and memory-dependent effect in the heat transfer process cannot be ignored. Many experimental and theoretical investigations suggest that, in practical analyses, thermal conductivity in materials should not be considered as a constant value. To compensate for such a deficiency, this work formulates a nonlocal thermoviscoelastic model with memory-dependent effect. This model integrates the fractional-order three-phase-lag (FTPL) heat conduction model and the nonlocal elasticity theory. The FTPL heat conduction model is based on the Caputo-Fabrizio (CF) definition of the fractional derivative, which does not have a singular kernel. In terms of application, the nonlinear electro-magneto-thermo-viscoelastic response of a polymer spherical nanoshell with variable thermal conductivity heated by a sinusoidal ultra-short pulse under the effect of a magnetic field is studied. Taking into account the variable thermal conductivity, the nonlinear governing equations are derived. The Laplace and Kirchhoff transformations are employed to derive and solve the governing equations that incorporate the fractional-order parameter, the nonlocal parameter and the variable thermal conductivity. The results show that the nonlinear thermoviscoelastic response of the polymer spherical microshell can be adjusted by the suitably modified parameters, which strongly depend on the size-dependent effect, memory-dependent effect and the variable thermal conductivity.</p>