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Molecular dynamics simulations are carried out to investigate the thermal and mechanical responses of GaN nanowires with the  orientation and hexagonal cross sections to tensile loading and unloading. The thermal conductivity of the nanowires at each deformed state is calculated using the Green-Kubo approach with quantum correction. The thermal conductivity is found to be dependent on the strain induced by tensile loading and unloading. Phase transformations are observed in both the loading and unloading processes. Specifically, the initially wurtzite-structured (WZ) nanowires transform into a tetragonal structure (TS) under tensile loading and revert to the WZ structure in the unloading process. In this reverse transformation from TS to WZ, transitional states are observed. In the intermediate states, the nanowires consist of both TS regions and WZ regions. For particular sizes, the nanowires are divided into two WZ domains by an inversion domain boundary (IDB). The thermal conductivity in the intermediate states is approximately 30% lower than those in the WZ structure because of the lower phonon group velocity in the intermediate states. Significant effects of size and crystal structure on mechanical and thermal behaviors are also observed. Specifically, as the diameter increases from 2.26 to 4.85 nm, the thermal conductivity increases by 30%, 10%, and 50%, respectively, for the WZ, WZ-TS, and WZ-IDB structured wires. However, change in conductivity is negligible for TS-structured wires as the diameter changes. The different trends in thermal conductivity appear to result from changes in the group velocity which is related to the stiffness of the wires and surface scattering of phonons.