In its 2016 Heating and Cooling Strategy, the European Commission (EC) highlighted the strategic importance of heating demand for the energy demand reduction, and further noted that District Heat Networks (DHN) can play an important role in decarbonising this sector. This study applied a thermal atlas approach to map the potential for district heat networks in Switzerland. It extended existing methods with a novel approach to estimating linear thermal demand density in DHN at a national scale. DHN potential for current-generation high temperature networks as well as cutting-edge low temperature networks were compared for current building space heating and hot water demand as well as for two demand reduction scenarios. The method was tested by comparing its results to those of a local engineering study conducted for a Swiss municipality (Brig-Glis). The potential percentage of demand supplied by high temperature DHN was shown to decrease from 66% to 41% with energy saving while the potential for low temperature systems increased significantly from 2.1% to 42%. The percentage of heat demand covered by heat networks decreases less than the percentage of buildings covered, reflecting the strength of heat networks for supplying large fractions of thermal demand in geographically confined areas.