We present phase coherence time measurements in quasi-one-dimensional Ag wires doped with Fe Kondo impurities of different concentrations n_{s}. Because of the relatively high Kondo temperature T_{K} approximately 4.3 K of this system, we are able to explore a temperature range from above T_{K} down to below 0.01T_{K}. We show that the magnetic contribution to the dephasing rate gamma_{m} per impurity is described by a single, universal curve when plotted as a function of T/T_{K}. For T>0.1T_{K}, the dephasing rate is remarkably well described by recent numerical results for spin S=1/2 impurities. At lower temperature, we observe deviations from this theory. Based on a comparison with theoretical calculations for S>1/2, we discuss possible explanations for the observed deviations.