Vibration-based monitoring (VBM) is widely applied for assessing the structural health of bridges, where tracking changes of modal characteristics is used for damage assessment. Natural frequencies are the most commonly employed modal characteristic for this purpose, but have the drawback that they are sensitive to temperature changes and not very sensitive to local stiffness variations. Recent case studies, primarily on steel railway bridges, have demonstrated that strain mode shapes offer a much higher sensitivity to local damage and are significantly less influenced by temperature. This study investigates the impact of temperature and solar irradiation on the natural frequencies and strain mode shapes of a post-tensioned concrete bridge used for vehicle traffic. For this purpose, a long-term monitoring campaign is performed, measuring operational dynamic strains and temperature. In agreement with existing case studies in literature, a significant impact of temperature and solar irradiation on the natural frequencies is observed. However, contrary to previous findings, also the strain mode shapes are found to be substantially temperature-dependent. This dependency is attributed to several factors: (1) the composite nature of the structure, where different materials have differing relationships between material properties and temperature, (2) the non-uniform temperature distribution caused by solar irradiation, and (3) the potential impact of changing support conditions and connections with varying temperatures. A finite element model was developed to capture these temperature-dependent effects, successfully replicating the observed temperature-induced changes in both natural frequencies and strain mode shapes. These findings suggest that composite bridges composed of diverse materials exhibit inherent variability in strain mode shapes, primarily due to their temperature dependency. For vibration-based damage detection, this implies that damage has to be sufficiently large to be detected through changes in strain mode shapes or neutral axis positions, if environmental variability is not accounted for.