Melt ponds form on Arctic sea ice in summer and autumn from the accumulation of snow and sea-ice meltwater and can cover up to 50% of the sea-ice surface. The presence of melt ponds has a profound impact on the surface albedo, contributing to the albedo feedback mechanism. When ponds freeze, the ice that forms on them insulates the pond trapping it between the sea ice and the ice lid. The trapped pond water stores a certain quantity of heat that is released with time. Trapped ponds have been observed in the Arctic and model simulations and observations show that they are present from a few months after the formation of the initial ice lid. We shall present a model of the thermal evolution of the sea ice, including the trapped meltwater, taking into account the effect of salt on the local freezing temperature of the trapped meltwater. We shall present simulation results showing the temperature profile in the meltwater, the freezing rate of the trapped meltwater and the evolution of the ice–air and ice–ocean interfaces.