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Climate change has several negative effects on health, including cardiovascular disease. Many studies have considered the effect of temperature on cardiovascular disease and found that there is an association between extreme levels of temperature, cold and hot, and cardiovascular disease. However, the number of articles that have studied the change point or the threshold in temperature is very limited. To the best of our knowledge, there have been no studies focusing on detecting and testing the significance of the change point in the temperature–cardiovascular relationship. Identifying the change point in cities may help to design better adaptive strategies in view of predicted weather changes in the future. Knowing the change points of temperature may prevent further mortality associated with the weather changes. Therefore, in this paper, we propose a unified approach that simultaneously estimates the semiparametric relationship and detects the significant point. A semiparametric generalized change point single index model is introduced as our unified approach by adjusting for several weather variables. A permutation-based testing procedure to detect the change point is introduced as well. A simulation study is conducted to evaluate the proposed algorithm. The advantage of our proposed approach is demonstrated using the cardiovascular mortality data of the city of Chicago, USA. [ABSTRACT FROM AUTHOR]