Abstract A simple model is used to examine the balance of heat, water flow and temperature in a long-lived single-pass hydrothermal system heated by magmatic heat. The geometry of the system is based on mid-ocean ridge observations. Cold water percolates downward to the top of a shallow magma chamber, is heated by conduction through a thin boundary layer, and discharges through a permeable fault zone, modelled as a bundle of narrow rough pipes. As heat input is increased, the model shows a catastrophic temperature transition at an exit water temperature of between 340 and 410°C depending on seafloor pressure, which in nature would probably be represented by surging flow and sudden changes in the specific volume of the circulating fluids. To generate a 3 million tonne sulphide deposit with 70% efficiency of deposition from water at 350°C within 4000 years would require a heat flux of 110 W m −2 from the magma chamber for a mass flow rate of 140 kg s −1, if the plan area of the reacting part of the system is 2 km 2. The total heat input would be 3 × 10 19 J. Under these conditions the thickness of the solid boundary layer between liquid magma and circulating water will be about 10 m, and the integrated reactive water-rock ratio over the lifetime of the system will be about 30. Decreasing the water temperature to 250°C would require a heat flux of only 60 W m −2, but the time to form a 3 million tonne deposit is increased to 33,000 years and the overall heat requirement is more than quadrupled.