We present a travel time formulation of water and energy transport at sub-catchment scale, resulting in a closed form solution for water temperature evolution in the subsoil compartment. The derived equations are implemented in Alpine3D, a physically-based model of snow processes, which provides the necessary boundary conditions to perform hydro-thermal response simulations of Alpine catchments. The model set-up accounts for advective and non-advective energy fluxes to perform spatially distributed simulations of streamflow and temperature in river networks having an arbitrary degree of geomorphological complexity. The model performance is illustrated comparing modeled and measured hydrographs and thermographs at the outlet of the Dischma catchment (45 km2) in the Swiss Alps. The model gives reliable predictions of streamflow and temperature. Our results suggest that the advective energy fluxes provide a large contribution to the thermal regime of the study catchment. The non-advective energy fluxes are also influential, as they contribute to cool the water in the winter and to warm it in the summer. The analysis of the distributed model results shows a notable streamflow spatial variability during a snowmelt event, as opposed to a more homogeneous response during a rainfall event. The stream temperature, instead, progressively increases from headwater streams to the outlet both during the snowmelt and the rainfall events. The proposed model completes the surface processes simulation framework of Alpine3D. The relevance of the work stems from the increasing scientific interest concerning the impacts of the warming climate on water resources management and temperature-influenced ecological processes.