An approximate Ornstein-Zernike equation [J. Chem. Phys. 114, 9496 (2001)] is used in order to analyze properties of a simple fluid in the vicinity of the critical point. The heat capacity and compressibility of the fluid are considered involving their relations with the density and temperature derivatives of the thermal potential (or the correlation function). A new structural critical exponent approaching zero value of the first nontrivial minimum of the total correlation function is defined. Using our approximate equation and that derived by Duh, Henderson, and Haymet [J. Chem. Phys. 103, 2625 (1995); 104, 6742 (1996)] a set of the thermodynamic parameters along the isotherm T* = 1.310, which is very close to the critical, is calculated. Computer simulation data are also given for comparison. (C) 2003 American Institute of Physics.