Although the processes by which glacial debris mantles alter the melting of glacier ice have been well studied, the mass balance and runoff patterns of Himalayan debris-covered glaciers and the response of these factors to climate change are not well understood. Many previous studies have addressed mechanisms of ice melt under debris mantles by applying multiplicative parameters derived from field experiments, and other studies have calculated the details of heat conduction through the debris layer. However, those approaches cannot be applied at catchment scale because distributions of thickness and thermal property of debris are heterogeneous and difficult to measure. Here, we established a runoff model for a Himalayan debris-covered glacier in which the spatial distribution of the thermal properties of the debris mantle is estimated from remotely sensed multi-temporal data. We applied the model to the Tsho Rolpa Glacial Lake–Trambau Glacier basin in the Nepal Himalaya, using hydro-meteorological observations obtained for a 3.5-year period (1993–1996). We calculated long-term averages of runoff components for the period 1980–2007 using gridded reanalysis datasets. Our calculations suggest that excess meltwater, which implies the additional water runoff compared with the ice-free terrain, from the debris-covered area contributes significantly to the total runoff, mainly because of its location at a lower elevation. Uncertainties in runoff simulation due to estimations of the thermal properties and albedo of the debris-covered surface were assessed to be approximately 8% of the runoff from the debris-covered area. We evaluated the sensitivities of runoff components to changes in air temperature and precipitation. As expected, warmer air temperatures increase the total runoff by increasing the melting rate; however, increased precipitation slightly reduces the total runoff, as ice melting is suppressed by the increased snow cover and associated high albedo. The response of total runoff to changing precipitation is complex because of the different responses of individual components (glacier, debris, and ice-free terrain) to precipitation.