We report the results of the x-ray radiative recombination (RR) experiment at the electron cooler of the ESR storage ring performed, for the first time, for detuned (off-cooling) electron energies. In this experiment the recombination of stored, decelerated bare uranium ions with electrons in the energy range 0–1000 meV was studied by observing K-RR x-ray photons emitted from direct radiative recombination to the lowest n=1 state. In this way the RR process was studied in a state selective manner for several off-cooling electron energies. The measured dependency of the recombination rate on the relative electron energies for K-shell RR x-ray photons are compared with the predictions of both nonrelativistic and fully relativistic calculations for the radiative recombination. A role of the relativistic effects, which contribute substantially for higher relative electron energies, are discussed. Strong enhancement of the recombination rate is observed for the the zero relative electron energy (cooling condition) for the K-shell.