Hydrothermal systems involving dormant faults within orogenic belts are rarely targeted for geothermal exploration, partly because of the complexity of the 3-D topography, the unknown permeability of the fault zones and the basement lithology, and the lack of deep-level data. This study brings together various types of surface information (spring features, geological data, topography, hydrochemistry) to explain the alignment of 29 hot springs (29-73°C) along the dormant Têt fault (Eastern Pyrénées, France). Water ion concentrations, stable water isotopes and lithium isotopic ratios indicate that (i) fluids originating from meteoric water infiltrate above an altitude of 2000 m, (ii) the rocks interacting with the fluids are similar for all the springs, and (iii) the maximum fluid temperatures at depth show similar variations along the fault and at the surface. A 3-D numerical model of the system, assembled from field structural data and from a Digital Elevation Model, explores the permeability combinations for the basement and for a three-fault network. The models indicate that for a relatively permeable basement (10-16 m2), fluids are topography-driven down to thousands of meters (until -3700 m) before being captured by the more permeable Têt fault. Hot spring temperatures can be numerically reproduced when fault permeability is around 10-14 m², a value slightly lower than the critical permeability for which free-convection would occur within the Têt fault. Our study shows that thermal anomalies are possible along dormant faults close to elevated topography in the core of an orogenic belt, thereby opening new perspectives for geothermal exploration.