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The Advection-Diffusion-Reaction equation is solved, applying the finite volume method, using high order discretisation schemes and flux limiting strategies that eliminate the false difusion and avoid spurious oscillations in the numerical solution. The algorithm is verified through benchmark tests with known exact solution, namely the cases of pure advection and pure diffusion, obtaining accurate results. A model for computation of the spatio-temporal distribution of the stream temperature in a 194 km long reach of the Biobo River, located in the Regin del Biobo of Chile, is elaborated. The study area includes from Rucalhue in the Andean chain at an elevation of 245 m to the river mouth in the Pacific Ocean. In the model, a detailed digital elevation model (DEM) of the river is used. Detailed hydrometeorologic records are taken from three measurement stations administrated by the National Water Agency, Direccin General de Aguas. For computation of the heat exchange between the stream water and the atmosphere, meteorological records obtained from four measuring stations are used, and an adequate spatially-distributed meteorological-database is elaborated. The instantaneous temperature distribution in the study reach is computed for the year 2003. The performance of the model is evaluated comparing the computations with detailed measurements of water temperature at the river mouth. Results exhibit the high accuracy of the model in the prediction of the stream temperature along the study reach, and show interesting aspects of river temperature dynamics as the influence of artificial reservoirs intended to hydropower generation