Enhancement in chemisorption is one of the active research areas in carbon materials. To remedy the thermally degraded chemisorption occurring at high temperatures, we report a comprehensive study of kink structures in free-standing monoatomic carbon nanowires upon heating. Our Monte Carlo simulation considers multi-monoatomic carbon chains laterally interacting by van der Waals forces. Our study reveals that carbon nanowires maintain their linearity regardless of chain length at low temperatures, but this is not the case at high temperatures. Disordered kink structure is observed in short carbon chains, especially above the Peierls transition temperature. A severe kink structure may increase the possibility of attaching negatively charged atoms, thereby contributing to the development of next-generation materials for chemisorption at high temperatures. We have also provided an important indication that any physical property of the finite-length carbon chain predicted by ab initio calculation should reconsider the atomic rearrangement due to thermal instability at high temperatures.