Two-thirds of submarine volcanism in the Earth's ocean basins is manifested along mid-ocean ridges and the remaining one-third is revealed along intraoceanic arcs and seamounts. Hydrothermal systems and the circulation patterns associated with these volcanic settings remove heat from the solid Earth into the deep ocean. Hydrothermal circulation continues to remove and redistribute heat in the crust as it ages. The heat and mass fluxes added to the deep ocean influence mixing in the abyssal ocean thereby affecting global thermohaline circulation. In addition to removing heat, hydrothermal processes extract chemical components from the oceanic and carry it to the surface of the ocean floor, while also removing certain elements from seawater. The resulting geochemical cycling has ramifications on the localized mineral deposits and also the biota that utilize these chemical fluxes as nutrients. In this dissertation, I analyze observed conductive heat flow measurements in the Panama Basin and borehole thermal measurements in Brothers Volcano and use mathematical models to estimate advective heat and mass fluxes, and crustal permeability. In the first manuscript, I use a well-mixed aquifer model to explain the heat transport in a sediment pond in the inactive part of the Ecuador Fracture Zone. This model yields mass fluxes and permeabilities similar to estimates at young upper oceanic crust suggesting vigorous convection beneath the sediment layer. In the second manuscript, I analyze the conductive heat flow measurements made in oceanic between 1.5 and 5.7 Ma on the southern flank of the Costa Rica Rift. These data show a mean conductive heat deficit of 70%, and this deficit is explained by various hydrothermal advective transport mechanisms, including outcrop to outcrop circulation, transport through faults, and redistribution of heat by flow of hydrothermal fluids in the basement. In the third manuscript, I analyze the borehole temperature logs for two sites representative of recharge and discharge areas of hydrothermal systems in the Brothers Volcano. I develop upflow and downflow models for fluids in the borehole and formation resulting in estimated of flow rates and permeabilities. All three independent research works are connected by the common thread of utilizing relatively simple mathematical concepts to get new insights into hydrothermal processes in oceanic crust.