Fresh water holds heat longer than salt water, because the addition of salt lowers the heat capacity of the solution relative to pure water. The lower heat capacity means that salt water both heats up and cools down more quickly than fresh water under the same conditions.
The heat capacity of a substance is the amount of heat needed to raise the temperature of a certain amount (usually 1 gram) of that substance by 1 degree C. It can be thought of as the substance's resistance to changes in temperature. If heat is applied at the same rate to a substance with a large heat capacity and a substance with a small heat capacity, the substance with the large heat capacity takes longer to increase in temperature.
When salt is dissolved in water, the resulting solution has a slightly lower heat capacity than that of fresh water. Due to the decreased heat capacity of salt water, if fresh water and salt water are heated to the same temperature and left to sit under the same ambient temperature and pressure, the fresh water takes longer to cool to a certain temperature than salt water. Thus, fresh water can be said to hold heat longer than salt water.