Thermal analyses of the response of offshore permafrost to emergence and submergence have traditionally employed simple closed-form solutions, where phase change is confined to a discrete freezing temperature. These have led to rather rapid rates of return to thermal equilibrium, which have proved difficult to explain in the light of recent deep temperature measurements in offshore permafrost profiles. This paper reviews the need for an appropriate unfrozen-water-content relationship for a saline frozen soil and describes some simulations of long-term thermal response in offshore permafrost using the author's geothermal simulator. Simulations of submergence assumed an initial permafrost thickness of 600 m and a mean soil-surface temperature of −9.0 °C. The salinity was assumed constant at 30‰. The initial-temperature profile was linear, varying between −9.0 °C and a freezing point of −1.8 °C at the bottom of ice-bonded permafrost. The temperature of the ground surface was assumed to have changed to −0.8 °C following submergence. After a period of 10 000 years, the predicted ground temperature at a depth of 300 m was −3.55 °C and was still rising. The equivalent temperature in a soil with a discrete freezing point would be 0.25 °C below the freezing point.Following permafrost submergence, for example, the rate of thaw in saline soils is somewhat faster than that predicted for discrete-freezing-point soils. However, more importantly, the rate at which the ground temperatures at depth rise in response to submergence is very much slower than that predicted by simpler closed-form solutions for freshwater soils. This means that for any given period since submergence, a cooler temperature profile would be predicted for a saline soil than for a soil with a discrete freezing point. This has far-reaching implications for geologists interpreting deep permafrost temperature records and for engineers involved with the design of structures in the arctic offshore.