The possibility of molten-salt freezing in pipe-flow systems is a key concern for the solar-energy industry and a safety issue in the new generation of molten-salt reactors, worthy of careful consideration. This paper tackles the problem of coolant solidification in complex pipe networks by developing a transient thermohydraulic model and applying it to the ‘Direct Reactor Auxiliary Cooling System’ (DRACS), the passive-safety system proposed for the Generation-IV molten-salt reactors. The results indicate that DRACS, as currently envisioned, is prone to failure due to freezing in the air/molten-salt heat exchanger, which can occur after approximately 20 minutes, leading to reactor temperatures above 900 °C within 4 hours. The occurrence of this scenario is related to an unstable behaviour mode of DRACS in which newly formed solid-salt deposit on the pipe walls acts to decrease the flow-rate in the secondary loop, facilitating additional solid-salt deposition. Conservative criteria are suggested to facilitate preliminary assessments of early-stage DRACS designs. The present study is, to the knowledge of the authors, the first of its kind in serving to illustrate possible safety concerns in molten-salt reactors, which are otherwise considered very safe in the literature. Furthermore, and from a broader prospective, the analytical tools developed in this study can also be applied to examine the freezing propensity of molten-salt flows in other complex piping systems where standard, finite element approaches are computationally too expensive.