In this study, the buckling behaviors of single-walled carbon nanocones (SWCNCs) under bending at finite temperatures are predicted using a proposed multiscale quasi-continuum approach based on the temperature-dependent higher order Cauchy–Born (THCB) rule. The hyper-elastic constitutive model is derived exactly in the context of the higher order gradient theory that incorporates the details of the interatomic interaction. The numerical simulations for the deformation of SWCNCs are implemented using the developed meshless computational framework based on moving least-squares interpolation, which can precisely reproduce the deformation process and buckling patterns of SWCNCs under bending. The underlying correlations of the critical bending angle with respect to the geometry of SWCNCs and temperature are revealed by the numerical results. Furthermore, our simulation captures the transformation from the local to the global buckling process of SWCNCs, accompanied with an average strain energy jump. Our results correspond with previous studies.