Banks face mounting pressure to integrate climate risks into lending, yet responses remain incoherent. This systematic literature review of 9034 studies synthesizes 68 peer-reviewed articles and develops a behavioral typology of five bank responses: recovery, containment, repricing, reallocation, and relational transformation. Responses vary by risk type, visibility, and salience. Acute, unexpected physical risks (nine studies) trigger recovery lending, while expected (five) or chronic risks (12) lead to containment or repricing. Transition risks (42) are more consistently priced when indicators are quantifiable and policy-aligned; softer ESG signals elicit conditional responses. Asymmetries arise: recovery and containment occur only for physical risks, while strategic reallocation remains rare. Carbon-intensive firms are penalized, while green firms benefit only when performance is credible and verifiable. We propose a diagnostic framework to evaluate climate risk management in lending, providing a novel tool to assess climate risk integration in bank lending and inform regulatory design and sustainability-oriented strategy.