Ground-state properties of a linear hydrogen-bonded FH ... NCH complex are studied by means of the "freeze-and-thaw" cycle of Kohn-Sham Equations with constrained electron density (KSCED) [T. A. Wesolowski and J. Weber, Chem. Phys. Lett. 248, 71, (1996)]. For several geometries of the complex, the electron density and the total energy are compared to the ones obtained by means of the standard Kohn-Sham calculations. The comparisons are made to assess the accuracy of several gradient dependent approximate kinetic energy functionals applied in the KSCED equations. It was found that the closest results to the Kohn-Sham ones were obtained with the functional whose analytical form was proposed by Perdew and Wang for exchange energy [J. P. Perdew and Y. Wang in Electronic Structure of Solids ’91, edited by P. Ziesche and H. Eschrig (Academie Verlag, Berlin, 1991), p. 11] and parametrized by Lembarki and Chermette for kinetic energy [A. Lembarki and H. Chermette, Phys. Rev. A 50, 5328 (1994)]. Around the interaction energy minimum as well as for larger intermolecular distances, the "freeze-and-thaw" cycle of KSCED leads to very similar potential energy surface as the standard supermolecule Kohn-Sham calculations.