Curved continuous steel box girders are extensively utilized in bridge construction due to its efficiency and environmental benefits. However, in regions with significant temperature fluctuations, temperature effects can result in cumulative deformation and stress concentration, which may severely impact structural safety and durability. This study examines the structural response of curved continuous steel box girders under diverse temperature conditions and also develops a comprehensive parameterized thermodynamic numerical model. The model assesses the influence of cross-sectional shape parameters including; the number of cross-sectional box chambers, diaphragm thickness, and height-to-width ratio, as well as longitudinal structural parameters such as planar configurations, width-to-span ratio, and support arrangements, along with the arrangement of stiffening ribs on the temperature-induced effects in the girders. Results indicate that optimizing the width and eccentricity of support stiffeners to 30% and 25% in the support plate size, respectively, can significantly alleviate local temperature-induced stresses. Additionally, variations in longitudinal and transverse stiffeners manifest minimal impact on thermal performance. These findings provide a theoretical foundation for improved design and construction practices, offering practical design recommendations to mitigate temperature effects and enhance the longevity and safety of such structures.