Reinjection of excess water from the power production process in Nesjavellir geothermal field has increased the temperature of the shallow groundwaters, posing a risk to cold water wells used for the power plant as well as the ecosystem in Lake Thingvellir. Here, we present a numerical model of the fluid flow and heat transport in the re-injection zone to elucidate the flow path of reinjected liquid and the impact of reinjection on the temperature of groundwaters. The permeability model is based on a 3D geological model of the area and the numerical simulation is calibrated against underground water temperature data measured between 1998-2018 and also data from a tracer test data performed in 2018-2019. We find that the dual-porosity approach is necessary to reproduce the fast and high tracer returns measured in some wells. The model reproduces the overall temperature field and shows how rift-parallel normal faults act as permeable channels controlling fluid transport. If injection continues, the temperature along the lava field increases considerably and spreads vertically to much deeper levels, generating a narrow warm zone along the main fault. If shallow injection ceases, the temperature drops rapidly at the surface, but around the reinjection zone temperatures decrease slowly and the subsurface temperature anomaly remains for the next 20 years. The numerical model in this study allowed a better characterization of the fracture matrix interface and the porosity of postglacial lava flows providing solutions for sustainable water management of the geothermal resource and the surrounding environment.