Definition of hot inner stellar halo advocated for and adopted in this paper. We show the stellar orbit distribution, p(r, λ_z), stellar age distribution, t(r, λ_z), and metallicity distribution, Z(r, λ_z), in the phase-space of circularity, λ_z, versus radius, r, of a simulated galaxy, TNG50 468590. We define as a hot inner stellar halo the galactic component whose stars have orbits with r_cut < r < r_max and λ_z < λ_z, cut, where r_cut, r_max, and λ_z, cut are, respectively, 3.5 kpc, max(7 kpc, 2 R_e), and 0.5.