With the increase in the utilization of nanomaterials in daily life, carbon nanostructures have received the attention of many researchers due to their special physical, chemical, and electrical properties. Chemical functionalization is one of the common methods to improve the thermomechanical properties of carbon nanomaterials used for specific applications. In this research, the effect of functionalization with hydrogen atoms on the mechanical properties of coiled carbon nanotubes with different geometrical dimensions has been examined. In addition, the mechanical properties of CCNTs with random and patterned distributions of hydrogen atoms have been investigated. The random distribution of hydrogen atoms up to 10% causes a sharp decrease in the mechanical properties of CCNTs such as the Young's modulus and spring constant, and increasing the percentage of H-coverage by more than 10% does not cause a significant effect on the mentioned properties. Also, unlike other carbon nanostructures, the stretchability of most CCNTs increases by increasing the percentage of hydrogenation beyond 30 percent. On investigating the effect of temperature on the properties of hydrogenated CCNTs, the temperature increase does not affect the Young's modulus and spring constant, and also there is no explicit relationship between their stretchability and temperature. Exploring the mechanical behavior of hydrogen-functionalized CCNTs via the tensile test and also how their mechanical properties change compared to those of pure CCNTs can help researchers in many applications.