In many coastal towns, sewage and industrial effluents are discharged via coastal outfalls into the sea. Here we study the discharge of an axisymmetric buoyant jet of less salty and colder wastewater into an unstratified stagnant sea to form a cloud of pollutant at the sea surface. We model the evolution of the temperature, salt and pollutant concentrations in the buoyant jet, polluted cloud and in the seawater surrounding the jet. The conservation equations are solved numerically. Our theoretical assumptions are supported by new experimental results. Two outfall scenarios corresponding to low and high stability of the interface between the seawater and the polluted stream are considered. We find that the interaction between double diffusion and turbulent entrainment into the buoyant jet results in a local accumulation of pollutant. When the interface stability is low, the pollutant concentration near the buoyant jet can increase by 100% compared with the magnitude expected in the absence of double-diffusion, in the timescale required for the polluted cloud to reach the coast. The effect of double diffusion on pollutant transport in the high-stability case is found to be small, as expected.