The study aims at providing comprehensive insights into the influence of the climatic stress on building heating demand. The examined case studies are two residential buildings, representative of the Italian existing and newly-built stocks, respectively. Building energy performance is simulated by comparing a standard normative approach with a tailored accurate one using EnergyPlus. The comparison is performed for several locations (i.e., 63) to consider all typical Italian climates. A global sensitivity analysis is performed to identify the most influential climatic parameters and to investigate the correlation between heating demand and HDD (heating degree days). The findings show that a base temperature of 18 °C in HDD assessment provides higher determination coefficient compared to 20 °C, and that HDD should consider also solar radiation and/or latitude to achieve a better correlation. Finally, climatic stress curves are provided to assess thermal energy demand and running cost for heating operation as a function of HDD for both the existing and the newly-built building.