The accurate prediction of the ice accretion on offshore structures or vessels caused by sea spray is important to ensure safe operations in the Arctic. Existing models of marine icing neglect the heat conduction of the accreted ice, which is reasonable only for continuous spray. However, marine spray is periodic and unsteady, and between spray events accreted ice cools below the freezing temperature of the spray. When a new spray arrives, it freezes primarily due to the heat release into the cold ice accreted before. In this paper, the ice accretion caused by periodic saline spray is studied experimentally and numerically. We present a new model which simulates the heat conduction inside the accreted ice and we show that entrapment of the unfrozen brine is modelled erroneously by the existing icing models.