In many European cities, heat demand remains mostly supplied by individual fossil fuel boilers, contributing to an inefficient and non-sustainable energy system. In order to decrease the fossil fuel consumption in the heating sector, an improvement of energy efficiency and an increase of renewable energy use must be achieved. This study assesses and compares the impacts of implementing different heat strategies regarding both demand and supply side of the heating system, through a case-study in the city of Geneva, Switzerland. Different heat scenarios for 2035 were developed, based on an input/output hourly energy system model which ensures the matching between heat demand and energy resources. This model is coupled with spatial data that enable to identify the areas where district heating could be developed. The results show the impacts of the different strategies regarding the energy supply, the CO2 emissions and the related socio-economic costs. The findings demonstrate the importance of district heating networks, which offer the possibility to use local heat sources that otherwise would be unused due to technical, spatial or economic constraints. Compared to a scenario essentially focused on very high energy savings in buildings, a more flexible scenario, combining district heating expansion and a smaller reduction in heat demand, enables to achieve the same reductions in fossil fuel consumption and CO2 emissions, but with lower socio-economic costs.