The present paper explains the temperature structure of X-ray emitting plasma in the core of the Perseus cluster based on 1.8–20.0 keV data obtained with the Soft X-ray Spectrometer (SXS) on board the Hitomi Observatory. A series of four observations was carried out, with a total effective exposure time of 338 ks that covered a central region of ∼7΄ in diameter. SXS was operated with an energy resolution of ∼5 eV (full width at half maximum) at 5.9 keV. Not only fine structures of K-shell lines in He-like ions, but also transitions from higher principal quantum numbers were clearly resolved from Si through Fe. That enabled us to perform temperature diagnostics using the line ratios of Si, S, Ar, Ca, and Fe, and to provide the first direct measurement of the excitation temperature and ionization temperature in the Perseus cluster. The observed spectrum is roughly reproduced by a single-temperature thermal plasma model in collisional ionization equilibrium, but detailed line-ratio diagnostics reveal slight deviations from this approximation. In particular, the data exhibit an apparent trend of increasing ionization temperature with the atomic mass, as well as small differences between the ionization and excitation temperatures for Fe, the only element for which both temperatures could be measured. The best-fit two-temperature models suggest a combination of 3 and 5 keV gas, which is consistent with the idea that the observed small deviations from a single-temperature approximation are due to the effects of projecting the known radial temperature gradient in the cluster core along the line of sight. A comparison with the Chandra/ACIS and the XMM-Newton/RGS results, on the other hand, suggests that additional lower-temperature components are present in the intracluster medium (ICM), but not detectable with Hitomi/SXS giving its 1.8–20 keV energy band.