The river-aquifer interaction in a 2-D scenario, in which heat transfer is coupled with water flow coming from the river to the aquifer, is numerically solved by the network simulation method providing the temperature-depth profiles.As regards temperature, seasonal (harmonic) variations are assumed at the soil surface, a free condition is imposed at the right boundary of outflow and a constant temperature is set at the bottom of the domain.For the flow, a permeable condition (reflecting a large domain) is imposed at the limits of the aquifer.The complexity of the temperature and stream function patterns, as well as the change in the standard (no flow) vertical and horizontal profiles is shown.From these patterns, some guides for the setting of the inverse problem that search the water flow from the river to the aquifer are proposed.