Central to achieving the energy transition, heating systems provide essential space heating and hot water in residential and industrial environments. A major challenge lies in effectively profiling large clusters of buildings to improve demand estimation and enable efficient Demand Response (DR) schemes. This paper addresses this challenge by introducing an unsupervised machine learning framework for clustering residential heating load profiles, focusing on natural gas space heating and hot water preparation boilers. The profiles are analyzed across five dimensions: boiler usage, heating demand, weather conditions, building characteristics, and user behavior. We apply three distance metrics: Euclidean Distance (ED), Dynamic Time Warping (DTW), and Derivative Dynamic Time Warping (DDTW), and evaluate their performance using established clustering indices. The proposed method is assessed considering 29 residential buildings in Greece equipped with smart meters throughout a calendar heating season (i.e., 210 days). Results indicate that DTW is the most suitable metric, uncovering strong correlations between boiler usage, heat demand, and temperature, while ED highlights broader interrelations across dimensions and DDTW proves less effective, resulting in weaker clusters. These findings offer key insights into heating load behavior, establishing a solid foundation for developing more targeted and effective DR programs.