We report the results of 151Eu Moessbauer effect and magnetization measurements in the Eu-doped Ca3Co2O6 and Ca3CoRhO6, which are of great current interest in the fields of spin-chain magnetism and geometrical frustration. We find that there is a pronounced increase in the line-width of the Moessbauer spectra below a certain characteristic temperature which is well-above the one at which three-diensional ordering features set in. This unusual broadening of the spectra indicates the existence of a characteristic temperature in these exotic magnetic systems, attributable to the onset of incipient one-dimensional magnetic order. This is inferred from an intriguing correlation of this characteristic temperature with the paramagnetic Curie temperature (a measure of intrachain coupling strength in these cases).