Geothermal heat is considered a sustainable energy source with significant global potential. Together with heat distribution networks, it can provide clean thermal energy to individual and commercial consumers. However, peaks in heat demand can require additional peaking sources at times. In this paper, we investigated how wind turbines can act as a peak energy source for a geothermal district heating system. We studied a model consisting of a geothermal heat source, a heat storage and wind power generator using historical weather data of Warsaw (Poland) and showed that wind power could increase the renewable share to supply a considerable heat demand compared to a geothermal heat source alone. The results indicate that wind power can be a suitable complement for a geothermal heat source to provide energy for heating. It is shown that a theoretical geo-wind-thermal storage based district heating network supplying 1000 m2, which requires 100 W/m2 at an outdoor temperature of −20 °C should have the following parameters: 4.8 MWh of thermal energy storage capacity, 45 kW of geothermal capacity and 5 kW of wind capacity. Such a system would ensure minimal wind curtailment, high utilization of geothermal source and high reliability of supply.