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This study investigates the influence of key temperature-dependent parameters on dengue transmission dynamics in Foz do Igua\u00e7u, a tri-border municipality in southern Brazil, using a mathematical model based on a system of ordinary differential equations. The fitted model aligns well with observed data. To track changes in dengue transmission over time and detect epidemic onset, we calculated the effective reproduction number. Additionally, we explored the potential effects of climate variability on dengue dynamics. Our findings highlight the importance of vector population dynamics, climate, and incidence, offering insights into dengue transmission in Foz do Igua\u00e7u. 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