Fermi liquid properties of nuclear matter at finite temperature are studied by employing a relativistic nonlinear (Ів, Іи) model of quantum hadrodynamics (QHD). The relativistic nonlinear (Ів, Іи) model is one of the thermodynamically consistent QHD approximations. The QHD approximations maintain the fundamental requirement of density functional theory (DFT). Hence, the finite temperature nonlinear (Ів, Іи) mean-field approximation can be self-consistently constructed as a conserving approximation. Fermi liquid properties of nuclear matter, such as incompressibility, symmetry energy, first sound velocity and Landau parameters, are calculated with the nonlinear (Ів, Іи) mean-field approximation, and contributions of nonlinear interactions and finite temperature effects are discussed. Self-consistent structure to an employed approximation as conserving approximation is essential to examine physical quantities at finite temperature. Finite-temperature effects are not large at high density, however, the Fermi ground state, density of states and Fermi-liquid properties may be varied noticeably with a finite temperature (TЁы10MeV) at low densities. Low-density finite-temperature and high-density finite-temperature experiments might exhibit physically different results, which should be investigated to understand nuclear many- body phenomena.