Physical climate risk has emerged as a critical source of financial instability, yet its integration into traditional credit risk models remains limited. Existing frameworks, particularly structural credit risk models, typically assume stable economic conditions and fail to account for persistent and cumulative environmental shocks. This creates a significant gap in the accurate estimation of corporate default probabilities, especially over long-term horizons. This study develops a dynamic credit risk model that explicitly incorporates physical climate risk into firm value dynamics. The model is formulated in discrete time, where firm value evolves as a stochastic process influenced by both financial shocks and a persistent climate risk factor. By introducing a climate sensitivity parameter, the framework captures the direct impact of environmental conditions on firm performance and creditworthiness. Analytical results demonstrate that climate risk systematically increases the probability of default. In particular, higher exposure to climate risk and greater persistence of climate shocks both lead to elevated default probabilities. The model also shows that ignoring climate risk results in consistent underestimation of long-term credit risk, with important implications for financial stability. Numerical simulations based on Monte Carlo methods illustrate how climate risk affects firm value trajectories and portfolio-level default behavior. The results highlight the role of climate risk as a common factor that induces correlation across firms, thereby amplifying systemic risk in bank loan portfolios. The proposed framework provides a transparent and mathematically tractable approach for incorporating physical climate risk into credit risk assessment. It offers practical relevance for banks and regulators seeking to enhance climate stress testing and improve long-term risk measurement in the financial system.