Climate risk has become an important challenge faced by economic entities, and exerted non-negligible impacts on firm decision-making. Based on the textual analysis with machine learning to construct firmlevel climate risk indicators, this paper explores the impact of climate risk on firms- cost stickiness using Chinese A-share listed firms with the period of 2014—2023. The results indicate that the climate risk significantly increases firm cost stickiness, and the adjustment costs, strengthened managerial risk expectations and exacerbated agency conflicts are the mechanisms between climate risk and cost stickiness. Furthermore, heterogeneity tests are carried out according to the different types of climate risks, industry attributes and firms- characteristics. The findings show that both physical risk and transition risk would increase firm cost stickiness. The association between climate risks and firm cost stickiness is more obvious in high-carbon industries, non-SOEs, and firms with lower ability to respond to risks. The economic consequence indicates that firm cost stickiness caused by climate risks adversely affects business operations, manifesting as increased business risks and a decline in firm sales profit margins. This paper expands the interdisciplinary research on climate risk and management accounting, which is conducive to relevant government departments to better assess and address climate risk, and also provides practical references for firms to cope with climate changes and effectively carry out cost management activities.