The ultrafast optical Kerr-response of water and heavy water has been measured at 1 bar in the temperature range between 273 and 373 K. The nuclear Kerr response of the liquid exhibits a pronounced double exponential decay on longer time scales after dephasing of impulsively perturbed acoustic modes is completed. The time constant, tau(2), characterizing the slowly decaying exponential component of the Kerr-response function is in quantitative agreement with rotational diffusion time constants of the water molecules obtained form nuclear magnetic resonance (NMR) spin-lattice relaxation rates. A detailed comparison with THz time domain spectroscopy demonstrates that the reorientational dynamics responsible for the long time tail of the Kerr response are due to single molecule as opposed to collective effects. Furthermore, a good agreement between the single molecule rotational diffusion and the Stokes-Einstein-Debye equation is found in the temperature range of thermodynamic stability of the liquid. The time constant, tau(1), characterizing the fast exponential component of the Kerr-response of water is found to be in qualitative agreement with central Lorentzian linewidths obtained from frequency-domain, depolarized Raman scattering experiments. The temperature dependence of tau(2) does not follow an Arrhenius-type behavior, which was previously taken as evidence for thermally activated crossing of a librational barrier with concomitant hydrogen-bond breakage. Instead, the temperature dependence of the fast relaxation time constant can be represented adequately by the Speedy-Angell relation which has been shown to accurately describe a number of transport parameters and thermodynamic properties of water.