Alkali metal lines are one of the most important key opacity sources for understanding exoplanetary atmospheres because the Na I resonance doublets are thought to be the cause of low albedo, as the alkali metal's wide line wings absorb almost all of the incoming stellar irradiation. High-resolution transmission spectroscopy of Na absorption lines can be used to investigate the temperature of the thermosphere of hot Jupiters, which is increased by stellar X-ray and extreme-ultraviolet irradiation. We applied high-resolution transmission spectroscopy to the ultra-hot Jupiter WASP-76 b with the High Dispersion Spectrograph (HDS) on the Subaru 8.2 m telescope. We report the detection of strong Na D excess absorption with line contrasts of $0.42 \pm 0.03\%$ (D1 at 5895.92 Å) and $0.38\pm 0.04\%$ (D2 at 5889.95 Å), full width at half maximum values of 1.63 ± 0.13 Å (D1) and 1.87 ± 0.22 Å (D2), and equivalent widths of (7.29 ± 1.43) × 10-3 Å (D1) and (7.56 ± 2.38) × 10-3 Å (D2). These results show that the Na D absorption lines are shallower and broader than those in previous work, whereas the absorption signals over the same passband are consistent with those in previous work. We derive the best-fitting isothermal temperature of 3700 K (without rotation) and 4200 K (with rotation). These results suggest the possibility of the existence of a thermosphere because the derived atmospheric temperature is higher than the equilibrium temperature (~2160 K).