The results of heat balance calculations for a single-pass hydrothermal system overlying an axial magma body, based on a given rate of heat output of 102--103 MW at a time to, product that vent temperatures should decay rapidly for t>to, as the magma freezes and the boundary layer between the hydrothermal system and liquid magma thickens. The model may describe a declining phase of high-temperature, high-heat-output hydrothermal activity. The model shows that for systems with heat output ~100 MW or greater, the boundary layer between the magma and hydrothermal system must remain thin, if vent temperatures remain relatively constant on a decadal timescale. A thin boundary layer can be maintained as a result of downward migration of the hydrothermal system into freshly frozen magma or by some mechanism that maintains high heat flux from liquid magma to the base of the boundary layer. Some combination of these factors is likely to operate. Downward migration of the hydrothermal system into freshly frozen magma may occur in conjunction with fracturing resulting from dike injection and the propagation of these cracks laterally away from the dike as a result of thermal stresses. High heat flux from liquid magma to the base of the hydrothermal system cannot be maintained simply by convection within the magma chamber. High heat flux might be maintained as a result of magma chamber replenishment or by latent heat transfer during the formation of a cumulate mush at the base of the magma chamber, however. A hydrothermal system, in which the permeability decreases with time, can maintain relatively constant vent temperatures even though the thermal output declines. Better time series data on thermal output of the vents, and not just on the vent temperature, could help distinguish whether the permeability is decreasing or whether heat flux as well as vent temperatures are relatively constant. ¿ American Geophysical Union 1994