The Lost City hydrothermal field (LCHF) is hosted in serpentinite at the crest of the Atlantis Massif, an oceanic core complex close to the mid‐Atlantic Ridge. It is remarkable for its longevity and for venting low‐temperature (40–91°C) alkaline fluids rich in hydrogen and methane. IODP Hole U1309D, 5 km north of the LCHF, penetrated 1415 m of gabbroic rocks and contains a near‐conductive thermal gradient close to 100°C km−1. This is remarkable so close to an active hydrothermal field. We present hydrothermal modelling using a topographic profile through the vent field and IODP site U1309. Long‐lived circulation with vent temperatures similar to the LCHF can be sustained at moderate permeabilities of 10−14 to 10−15 m2 with a basal heatflow of 0.22 W m−2. Seafloor topography is an important control, with vents tending to form and remain in higher topography. Models with a uniform permeability throughout the Massif cannot simultaneously maintain circulation at the LCHF and the near‐conductive gradient in the borehole, where permeabilities <10−16 m2 are required. A steeply dipping permeability discontinuity between the LCHF and the drill hole is required to stabilize venting at the summit of the massif by creating a lateral conductive boundary layer. The discontinuity needs to be close to the vent site, supporting previous inferences that high permeability is most likely produced by faulting related to the transform fault. Rapid increases in modelled fluid temperatures with depth beneath the vent agree with previous estimates of reaction temperature based on geochemical modelling.