In this paper, the thermal buckling characteristics of armchair single-walled carbon nanotube (SWCNT) embedded in a one-parameter elastic medium are investigated using a new nonlocal first-order shear deformation theory (NNFSDT). The present model is able to consider the small-scale effect as well as the transverse shear deformation effects of nanotubes. The equivalent Young’s modulus and shear modulus for armchair SWCNT are obtained by employing the energy-equivalent model. A closed-form solution for nondimensional critical buckling temperature is obtained in this investigation. The results illustrated in this work can provide a significant guidance for the investigation and design of the novel generation of nanodevices that make use of the thermal buckling characteristics of embedded SWCNT.