This article introduces a technique for three-dimensional inverse modeling of geothermal heat conduction through heterogeneous media. The technique is used to determine the basal geometry of a diapiric salt structure found on the continental slope offshore Texas. Salt is two to four times more thermally conductive than other sedimentary rocks. The geothermal field is perturbed by the presence of salt and results in an anomaly in the heat flow through the seafloor. The spatial variation pattern of the anomalous heat flow reflects the geometry of the salt body. The inverse modeling obtains a model for the thermal-conductivity structure that causes the heatflow anomaly observed on the seafloor. The inversion algorithm systematically searches for an optimal thermal-conductivity model by iteratively minimizing the misfit between the model-predicted and the observed heat flow. To reduce the problem of nonuniqueness, the inversion incorporates a priori information constrained independently, such as the upper surface geometry of the salt and the lateral extent of the salt body, which can be delineated by a limited coverage of two-dimensional seismic data. In addition, it is assumed that the thermal conductivity of the sedimentary strata surrounding the salt body is well constrained. This inversion method is applied to a heat-flow data set obtained over a salt structure on the Texas continental slope. The salt structure was first surveyed with the single-channel seismic reflection, which yielded the a priori information necessary. The base of the salt was not imaged seismically. Then, three dozen heat-flow measurements were obtained on the seafloor over and off the salt feature. The inverse heat-flow modeling performed here shows that this structure is a salt tongue, which has a diapiric root on one side. According to the most optimal thermal-conductivity model obtained, the root seems to extend to 6 km below the seafloor. Refinement in the model geometry and additional constraints on thermal conductivities of the surrounding strata should yield a model that is more detailed and would allow more thorough geological interpretation of the salt structure.