We report on the calculations of radiative recombination (RR) rate coefficients for very low, in the range of a few meV, relative electron-ion energies. The rate coefficients are derived for bare lead ions colliding with free electrons in a rigorous relativistic manner, in which all multipoles of electron-photon interaction under the inclusion of retardation effects are taken into account. We demonstrate that the measurements of absolute rate coefficients at electron cooler devices are really sensitive to the high Rydberg states, as well as to the transverse electron temperature 𝑘𝑇 ⊥ and the longitudinal electron temperature 𝑘𝑇 ∥ .