This paper examines the effect of temperature on the structural stability and mechanical properties of 20-layered (10,10) single-walled carbon nanotubes (SWCNTs) under tensile loading using an O(N) tight-binding molecular-dynamics simulation method. We observed that (10,10) tube can sustain its structural stability for the strain values of 0.23 in elongation and 0.06 in compression at 300 K. Bond-breaking strain value decreases with increasing temperature under stretching but not under compression. The elastic limit, Young's modulus, tensile strength, and Poisson ratio are calculated as 0.10, 0.395 TPa, 83.23 GPa, and 0.285, respectively, at 300 K. In the temperature range from 300 to 900 K, Young's modulus and the tensile strengths decrease with increasing temperature while the Poisson ratio increases. At higher temperatures, Young's modulus starts to increase while the Poisson ratio and tensile strength decrease. In the temperature range from 1200 to 1800 K, the SWCNT is already deformed and softened. Applying strain on these deformed and softened SWCNTs does not follow the same pattern as in the temperature range of 300 to 900 K.