Styrene-butadiene copolymers are modified with varying fractions of benzoic acid moieties being able to perform hydrogen bonding. This is done by using a simple synthetic approach which utilizes click chemistry. Temperature-dependent dynamic mechanical properties are studied, and it turns out that even the apparently rather simple hydrogen bonding motif has a marked impact on the material properties due to the fact that it facilitates the formation of a supramolecular polymer network. Besides a glass transition, the investigated functionalized copolymers exhibit a second endothermic transition, known as a quasi-melting. This is related to the opening of the hydrogen bonding complexes. Additionally to dynamic mechanical analysis (DMA), differential scanning calorimetry (DSC), temperature-dependent infrared (IR) spectroscopy and small angle X-ray scattering (SAXS) are used to understand the structure-property relationships.