Monte Carlo simulations in the NW ensemble of the reference hard-sphere fluid have been performed to obtain the "exact" first- and second-order terms in the inverse temperature expansion of the free energy of fluids with hard-core potentials. The results have been used to obtain parametrizations of the free energy of fluids with Sutherland potentials with variable range as well as for a fluid with a hard-core Lennard-Jones potential. The results for the excess energy and the equation of state are compared with simulation data available in the literature for these fluids. (C) 2010 Elsevier B.V. All rights reserved.