Properties of FeTe0.65Se0.35 single crystals, with the onset of critical temperature (Tc^onset) 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 Tc^bulk, 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 Tc^bulk 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.