As a complex thermal network ensuring civil and industrial energy supply, the failure of key components in heating systems can easily trigger cascading failures and large-scale heating outages. Aiming at the high computational complexity of traditional failure-simulation-based methods for key component identification, this study proposes a multi-dimensional index system and identification framework integrating graph-theoretic topology analysis and thermodynamic function evaluation. By constructing a modified betweenness index (topological importance), energy index and residual energy ratio (functional importance), and combining with system flow loss rate and user flow loss entropy (failure consequence indices), a complete quantitative evaluation system is formed. Verification using gridded heating system models with 4 to 25 nodes shows that the Spearman correlation coefficients between the modified betweenness and user flow loss entropy range from 0.82 to 0.93, and those between the energy index and system flow loss rate range from 0.65 to 0.96, with all coefficient of variation values less than 0.1, verifying the effectiveness and stability of the indices. The research results provide theoretical support for the efficient and accurate identification of key components in heating systems.