Hybrid density functional theory calculations are performed for the first time on the phonon dispersion and thermodynamic properties of WS₂-based single-wall nanotubes. Symmetry analysis is presented for phonon modes in nanotubes using the standard (crystallographic) factorization for line groups. Symmetry and the number of infra-red and Raman active modes in achiral WS₂ nanotubes are given for armchair and zigzag chiralities. It is demonstrated that a number of infrared and Raman active modes is independent on the nanotube diameter. The zone-folding approach is applied to find out an impact of curvature on electron and phonon band structure of nanotubes rolled up from the monolayer. Phonon frequencies obtained both for layers and nanotubes are used to compute the thermal contributions to their thermodynamic functions. The temperature dependences of energy, entropy, and heat capacity of nanotubes are estimated with respect to those of the monolayer. The role of phonons in the stability estimation of nanotubes is discussed based on Helmholtz free energy calculations.