This paper utilizes molecular-dynamics simulations to investigate the mechanical characteristics of a suspended (10, 10) single-walled carbon nanotube (SWCNT) during atomic force microscopy (AFM) nanoindentation at different temperatures. Spontaneous topological transition of the Stone-Wales (SW) defects is clearly observed in the indentation process. The present results indicate that under AFM-bending deformation, the mechanical properties of the SWCNT, e.g., the bending strength, are dependent on the wrapping angle. In addition, it is also found that the radial dependence of the reduced formation energy of the SW defects is reasonably insensitive only for the small tubes. However, for tube diameters greater than 2.4 nm [corresponding to the (18, 18) CNT], the SW defects tend to be more radius sensitive. The results indicate that the bending strength decreases significantly with increasing temperature. This study also investigates the variation in the mechanical properties of the nanotube with the density of C60 encapsulated within the nanotube at various temperatures. It is found that, at lower temperatures, the bending strength of the C60-filled nanotube increases with C60 density. However, the reverse tendency is observed at higher temperatures. Finally, the "sharpest tip" phenomena between the probe and the tube wall and the elastic recovery of the nanotube during the retraction process are also investigated.