This study examines how ESG integration and climate-related financial risk are represented in a selected sustainable-finance literature corpus. It combines reported bibliometric outputs for 27 records with a Theory–Context–Characteristics–Methodology (TCCM) synthesis of 23 studies. The annual publication counts increase from three in 2022 to nine in 2025, while the reported country citation table is concentrated in India. The thematic synthesis identifies substantial attention to ESG investing, green bonds, sustainability reporting and digital finance. Physical and transition risks receive limited explicit attention within the supplied coding, but this sample-level observation does not establish their absence from the wider literature. After correcting one study classification, the working methodological distribution comprises 11 bibliometric or scient metric studies, nine other reviews, two conceptual studies and one empirical study. The synthesis distinguishes established theories from organising frameworks and topic labels, and develops a research agenda linking climate exposure, disclosure quality and financial outcomes. Interpretation remains conditional on reconciliation of the 27-record bibliometric dataset with the 23-study coding set and recovery of the search and screening audit trail. The contribution is therefore a focused, provisional evidence synthesis and a more explicit agenda for integrating climate-risk analysis into ESG research.