The decarbonisation of the building heating sector requires a shift from decentralised fossil fuel heating appliances to systems converting energy carriers with low greenhouse gas (GHG) emissions. However, for certain energy carriers, a considerable portion of GHG emissions arises upstream during production, processing and transportation, rather than during energy conversion. Accurately quantifying these indirect GHG emissions typically requires life cycle assessments, which are often resource-intensive and impractical during the early stages of energy system design. This study introduces operational GHG emissions as a pragmatic metric for the preliminary assessment of energy carrier environmental impact in building heating applications. These operational GHG emissions include both direct CO2 emissions and indirect CO2, CH4 and N2O emissions. Based on a comprehensive literature analysis, average estimates are proposed for the operational GHG emissions of various energy carriers within a European context, including natural gas, oil, coal and wood, as well as the average European and Belgian electricity grid, and hydrogen from various production methods. The findings underscore the significant contribution of indirect GHG emissions, as the selection of the energy carrier with the lowest environmental impact hinges on whether direct emissions alone or the broader operational GHG emissions are considered. By integrating operational GHG emissions into the early design stages of energy systems, stakeholders can make more informed decisions about which energy systems warrant further investigation, thereby facilitating more sustainable energy system development from the outset.