Summary: The thermodynamic quantities of a many-fermion system at low excitation energy are studied in terms of the temperature-dependent antisymmetrized density matrices in spherical and spheroidally deformed harmonic oscillator potentials at quite low temperature. The internal energies of the canonical ensemble of many fermions coincide numerically with those of microcanonical ensemble in the same spherical HO potentials. The saturation properties of binding energy per fermion are found partly as effects of deformation. The relationship between this treatment and the liquid drop model is studied. The characteristic feature of the liquid drop model is found to be not inconsistent with this treatment.