The contribution of the 4f electron to the local magnetic field at highly diluted Ce atoms in RERh(2)Si(2) (RE = Ce, Pr, Nd, Gd, Tb, Dy) has been investigated as a function of temperature through the measurement of the magnetic hyperfine field in (140)Ce nuclei by time differential perturbed gamma-gamma angular correlation spectroscopy. Samples of the studied compounds were characterized by x-ray diffraction and zero-field resistance to determine the crystal structure and transport properties. DC magnetic susceptibility was measured for NdRh(2)Si(2). It was observed that the variation of the magnetic hyperfine field with temperature follows the expected behaviour for the host magnetization, with the exception of GdRh(2)Si(2), which showed a strong deviation from such a behaviour. It is shown that the hybridization of the d band of the host with the f band of the Ce impurity, which is stronger in GdRh(2)Si(2) than in other compounds, is responsible for the observed deviation from the expected temperature dependence of the hyperfine field. The origin of this stronger hybridization is ascribed to the relatively small magnetic anisotropy observed in GdRh(2)Si(2) when compared with the other compounds of the series, as shown by resistance measurements.