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Abstract The horizontal salt cavern is the ideal place for energy storage built in bedded salt formations. The construction of the multi-step horizontal salt cavern is a complicated process of fluid dynamics and chemical dynamics, including salt boundary dissolution, cavern development, brine flow, heat transfer, and species transport. Considering the influence of the heat transfer, the multiple governing equations are coupled to simulate the construction process of the 3D horizontal salt cavern. The influence of heat transfer on fluid flow, brine concentration, and cavity expansion is analyzed. According to the results, heat transfer accelerates the transport and diffusion of the brine, which can increase the dissolution rate of salt rock. The direction of the forced thermal convection is perpendicular to the direction of fluid flow and the brine concentration gradient in the cavity. The results also show that the formed cavity previously will continue to expand in the next leaching stage, but the height of expansion decreases gradually. This work helps predict the multi-step horizontal salt cavern development and concentration distribution under reasonable accuracy, which may guide to the scheme design and engineering practice of the multi-step horizontal salt cavern construction for underground gas storage.