Mountain topography creates variations in water-table elevation that drive groundwater flow. Consequently, advective heat transport by topography-driven fluid flow can modify the crustal thermal field and bias exhumation rates calculated from thermochronometer data. Although previous studies have considered the thermal effects of fluid flow, none has quantified the influence on thermochronometer ages. We use a steady-state three-dimensional coupled hydraulic thermokinematic finite-element model to simulate the influence of fluid flow on exhumation rates derived from thermochronometer data in the Nepalese Himalaya. Local hot springs suggest substantial heat transport by fluid flow and are adjacent to apatite fission-track samples. Model hydraulic conductivity controls the rate of fluid flow, and values characteristic of fractured rock (>>10−9 m/s) yield a fluid advection–dominated thermal field. Hydraulic conductivity is estimated by minimizing the misfit between predicted and observed hot spring thermal power. The best-fit hydraulic conductivity value of ∼5 × 10−7 m/s produces a fluid advection–dominated thermal field and older predicted apatite fission-track ages. To fit the observed age-elevation relationship, model-predicted ages require denudation rates that are ∼5 mm/yr, ∼200% higher than predictions from thermal models that do not simulate fluid flow. Thus, true exhumation rates can be substantially underestimated in orogenic systems where fluid advection is significant.