Four types of linear thermal expansion coefficients of helically coiled carbon nanotubes (radial tubular, axial tubular, helical radial and helical axial) are numerically evaluated by minimizing Helmholtz free energy at fixed temperatures. Isotropy of thermal expansion of tubular parameters and high anisotropy of thermal expansion of the coil parameters are predicted. The latter is interpreted by spring like behavior and extreme elasticity of helically coiled carbon nanotubes. Brenner interatomic potential for carbon is used. Applied also is the line group symmetry which together with Hooke–Jeeves algorithm made the calculations highly efficient.