Currently, most of the modern concentrated solar thermal power plants employ molten salts as the heat transfer fluid to carry the thermal energy from solar concentrators and deliver to thermal storage systems or thermal power plants for the need of power generation. For the startup operation of solar concentrators, molten salts need to be pumped to flow into the pipes which may have lower temperature than the molten salt due to cold ambient overnight or over the suspend period of operation. As the freezing point of various molten salts ranges from 220 °C to 430 °C, preventing the freezing of molten salt flowing in cold pipe is a very important requirement for the safe operation of a concentrated solar thermal power plant. In this work, the authors have conducted a basic heat transfer analysis of transient heat exchange between molten salts and the flow pipe to find a criterion or the critical condition of preventing molten salt from freezing. The effects of molten salt flow velocity, heat capacities of molten salt and pipe, dimensions of pipes, and the initial temperatures of salts and cold pipes are all correlated theoretically in the analysis through modeling of transient heat transfer between a pipe and the fluid. The results are very helpful to the understanding and management of a safe startup of hot molten salt flowing in cold pipes on cyclic operations.