Given the intermittent nature of renewable energy sources (e.g., solar and wind) and the volatility of energy prices, the adoption of energy storage solutions has become increasingly vital. Thermal energy storage systems hold a pivotal role in enabling penetration of renewable energy sources and decarbonization of process heat. In this thermodynamic analysis, a series of calculations were conducted to delve into the charging and discharging dynamics of a thermal energy storage system, which utilizes desalination salt as storage material and works in conjunction with a low-temperature thermal desalination system. Desalination salt is an inevitable byproduct of ocean water or brackish water desalination processes. A thermodynamic model was developed to study the transient behavior of thermal storage integration during charge and discharge cycles. During the charge cycle an oil heater provided the required heat either at constant temperature or constant heat transfer rate to the heat transfer fluid and subsequently, during the discharge cycle, heat transfer fluid serves as the medium for transporting energy from the thermal energy storage device to a heat exchanger that feeds the thermal desalination unit. Our investigation explores two discharge scenarios, i.e., with and without a bypass loop, allowing for more control on the discharge temperature. The results show that the duration of the discharge at the desired temperature can be optimized by controlling maximum storage temperature of the storage material and charge and discharge cycle flow rates of heat transfer fluid.