Herein, we describe the design and synthesis of a new variety of bio-based hydrogel films using a Cu(I)-catalyzed photo-click reaction. These films exhibited thermal-triggered swelling-deswelling and were constructed by crosslinking a triazide derivative of glycerol ethoxylate and dialkyne structures derived from isosorbide, a well-known plant-based platform molecule. The success of the click reaction was corroborated through infrared spectroscopy (FTIR) and the smooth surface of the obtained films was confirmed by scanning electron microscopy (SEM). The thermal characterization was carried out in terms of thermogravimetry (TGA) and differential scanning calorimetry (DSC), from which the decomposition onset and glass transition temperatures were determined, respectively. Additionally, mechanical properties of the samples were estimated by stress-strain experiments. Then, their swelling and deswelling properties were systematically examined in PBS buffer, revealing a thermoresponsive behavior that was successfully tested in the release of the anticancer drug doxorubicin. We also confirmed the non-cytotoxicity of these materials, which is a fundamental aspect for their potential use as drug carriers or tissue engineering matrices.