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Because climate change broadcasts a large aggregate risk to the overall macroeconomy and the global financial system, we investigate how a temperature anomaly and/or its volatility affect the accuracy of forecasts of stock return volatility. To this end, we do not apply only the classical GARCH and GARCHX models, but rather we apply newly proposed model-free prediction methods, and use GARCH-NoVaS and GARCHX-NoVaS models to compute volatility predictions. These two models are based on a normalizing and variance-stabilizing transformation (NoVaS transformation) and are guided by a so-called model-free prediction principle. Applying the new models to data for South Africa, we find that climate-related information is helpful in forecasting stock return volatility. Moreover, the novel model-free prediction method can incorporate such exogenous information better than the classical GARCH approach, as revealed by the the squared prediction errors. More importantly, the forecast comparison test reveals that the advantage of applying exogenous information related to climate risks in prediction of the South African stock return volatility is significant over a century of monthly data (February 1910–February 2023). Our findings have important implications for academics, investors, and policymakers.