The clean heating compound transformation under the Carbon Neutrality Goal is necessary for the high-quality development of the heating industry in China. Based on the literature analysis, questionnaires and semi-structured interviews, this paper identifies 15 driving factors affecting the transition at three levels: technology, organization and environment. This paper introduces Fuzzy Set Theory into Decision-Making Trial and Evaluation Laboratory method, and combined with explanatory structural models to form a combined Fuzzy-DEMATEL-ISM approach. Using the Fuzzy-DEMATEL-ISM method to analyze the degree of influence, hierarchical relationships and logical associations among the influencing factors to reveal the influence mechanism of the compound transition of clean heating. The results show that 1) the key influencing factors for the transition are energy use and delivery methods, heating system operation and maintenance management, and clean heating costs and expenses. 2) There are eight causal factors and seven consequential factors in the clean heating compound transition influence factor system. 3) The recursive structure model of influencing factors is divided into five levels from bottom to top: root level, deep level, middle level, shallow level and surface level, among which environmental and clean heating policies, clean heating technology innovation level and resource endowment status are the basic guarantees of transformation. It provides a theoretical supplement and practical guidance for the compound transition to clean heating under the carbon neutrality goal.