By providing demand-side flexibility without any service interruption, hybrid heating systems can foster the integration of non-dispatchable renewable energies into the power grid and avoid greenhouse gas emissions from carbonized electricity production. However, such systems are not yet controlled by a signal providing the marginal CO2 content of the avoided electricity production as few studies inquired this point in details. In this article we show that a pool of hybrid heat pumps, supplied alternatively with electricity or with gas do minimize the carbon intensity of heating. For this purpose, an urban energy model was used to generate the heating demand of 100 000 dwellings throughout France and the electricity system was modeled based on priority lists with constraints for scheduling and dispatching the electricity generated by the power plants. The marginal electricity mix corresponding to a pool of 100 000 heat pumps and the corresponding activation time for a gas boiler were evaluated.