Hydrothermal processes at oceanic spreading centers are largely influenced by changing magmatic heat input. I use the FISHES code to investigate the evolution of surface temperature and salinity as a function of time-varying heat flux at the base of a two-phase, vapor-brine hydrothermal system. I consider a two-dimensional rectangular box that is 1.5 km deep and 4 km long with homogeneous permeability. Impermeable, insulated conditions are imposed on the left and right hand boundaries. To simulate time-varying heat flux from a sub-axial magma chamber of 500 m long half-width, I consider a variety of basal boundary conditions: (1) a constant heat flux with an value of 130 W/m2; (2) a sinusoidal heat flux with a period of 6 years and an amplitude ranging between 100 and 50 W/m2; (3) step, random, and exponential heat fluxes ranging between 200 and 15 W/m2; and (4) an analytical function of temporally decaying heat flux resulting from a simulated cooling, crystallizing magmatic sill. As a result of the investigation I find: (1) changes in bottom temperature and salinity closely follow the temporal variations in magmatic heat inputs; (2) the surface temperature response is severely damped and high frequency variations in heat flow are not detected; (3) in regions where phase separation of vapor and brine occurs, surface salinity variations may be recorded in response to changing conditions at depth, but these are smaller in amplitude. / Master of Science