The integrity and stability of salt caverns for natural gas storage are subjected to a gas cycling loading operation. The coupled effect of confining pressure and temperature on the response of the salt cavity surrounding the wall is essential to stability analysis. In this study, a hybrid continuum-discrete model accounting for the thermal-mechanical process is proposed to investigate the thermal-damage evolution mechanism towards a field case with blocks falling off the salt cavity. The salt cavity is modeled by continuum zones, and the potential damage zones are simulated by discrete particles. Three specimens at different locations around the surrounding wall are compared in the context of severe depressurization. The dynamic responses of rock salt, including temperature spatiotemporal variation, microscopic cracking patterns, and energy evolution exhibit spatial and confinement dependence. A series of numerical simulations were conducted to study the influence of microproperties and thermal properties. It is shown that the evolution of cracks is controlled by (1) the thermal-mechanical process (i.e., depressurization and retention at low pressure) and (2) the anomalous zone close to the brim of the salt cavity surrounding the wall. The zone far away from the marginal surrounding wall is less affected by temperature, and only the mechanical conditions control the development of cracks. This continuum/discontinuum approach provides an alternative method to investigate the progressive thermal damage and its microscopic mechanism.