Global warming and frequent extreme weather have rendered climate risks a key factor affecting corporate financial performance. This study explores how climate risk correlates with firms’ cost of debt financing and its underlying transmission channels. We take China’s A-share listed firms from 2016 to 2024 as samples, construct a climate risk index covering physical and transition risks via annual report text mining, and adopt two-way fixed-effect regressions for baseline analysis. We perform mediating mechanism tests to identify transmission paths, and conduct multiple robustness checks along with instrumental variable estimation and propensity score matching (PSM) to address potential endogeneity concerns. Subgroup analyses are conducted based on information disclosure quality, firm size and industrial carbon features. Results show climate risk is positively associated with higher cost of debt financing. Two mediating pathways are verified: climate risk reduces corporate solvency and elevates operational volatility, which pushes up the cost of debt financing. The positive correlation is more pronounced for enterprises with low information disclosure quality, large firms, and low-carbon industries, while high-carbon firms show insignificant responses. The findings offer supplementary empirical evidence on climate-related cost of debt financing. Relevant suggestions for firms and regulators are provided to improve climate risk management and green financial governance under the dual-carbon framework.