Properties of FeTe0.65Se0.35 single crystals, with the onset of critical temperature (Tconset) at 15.5 K, were modified via hydrogenation performed for 10–90 h, at temperatures ranging from 20 to 250 °C. It was found that the tetragonal matrix became unstable and crystal symmetry lowered for the samples hydrogenated already at 200 °C. However, matrix symmetry was not changed and the crystal was not destroyed after hydrogenation at 250 °C. Bulk Tcbulk, determined at the middle of the superconducting transition, which is equal to 12–13 K for the as grown FeTe0.65Se0.35, rose by more than 1 K after hydrogenation. The critical current density studied in magnetic field up to 70 kOe increased 4–30 times as a consequence of hydrogenation at 200 °C for 10 h. Electron paramagnetic resonance measurements also showed higher values of Tcbulk for hydrogenated crystals. Thermal diffusion of hydrogen into the crystals causes significant structural changes, leads to degeneration of crystal quality, and significantly alters superconducting properties. After hydrogenation, a strong correlation was noticed between the structural changes and changes in the parameters characterizing the superconducting state.