The extended law of corresponding states was proposed based on the patterns observed in the second virial coefficient for potential models of variable range. In this work, we propose the use of this law, together with a generalized Lennard-Jones (or approximate nonconformal, ANC) potential, to predict the critical temperatures of real fluids. To this end, we first observe that the temperatures obtained from the scaling law are in agreement with those obtained from molecular simulations of ANC fluids. For short ranges, however, validation is performed by mapping the ANC fluid to the square well fluid because no simulation data have been reported for the former fluid for these ranges. Overall, the analysis shows the validity of the scaling law and the ANC potential for predicting critical temperatures for any range. With this in mind, the well depths of the effective binary potentials of atoms and molecules are rescaled to apply a correction for the three-body nonadditive interaction in order to determine the critical temperatures of fluids.