We have performed a detailed study of the temperature dependence and of the isotropic-nematic phase transition in a fluid of moderately long elongated molecules interacting via a Gay - Berne potential with anisotropy parameters x(0) = 4.4; k' = 20.0, mu = 1; and nu = 1: The nematic phase is found to be stable with respect to the isotropic phase for reduced temperatures T* <= 1.60. In the temperature range 1.60 <= T* <= 3.0, the phase boundaries of the isotropic - nematic transition are obtained by using the density-functional theory. The pair-correlation functions of the isotropic phase that enter in the density-functional theory as input informations are found from the Percus-Yevick integral equation theory. The accuracy of the Percus-Yevick integral equation theory has been tested by comparing the pair-correlation functions of the Gay - Berne fluids with computer simulation results. The density-functional theory is good enough to study the freezing parameters of complex fluids if the values of the pair-correlation functions of the isotropic phase are known accurately.