We present new measurements of hydrated electron mobility in both H2O and D2O for the full liquid temperature range at atmospheric pressure. Transient conductivity signals were measured following pulse radiolysis of aqueous alkaline solutions with 16-MeV electrons. The conductivity signal is proportional to the difference in specific conductance of the electron and the hydroxide (or deuteroxide) ion. To evaluate the signals in heavy water, ancillary measurements of the electron radiolysis yield vs temperature were made. The specific conductance of OD- in heavy water is estimated using (light water) transfer numbers and tabulated here for the first time. In H2O, the hydrated electron specific conductivity is found to be 184.0 +/- 0.7 S cm2 at 298 K, giving a diffusion coefficient of (4.90 +/- 0.02) x 10(-5) cm2/s with an average activation energy in the temperature range 15-90-degrees-C of 4.81 +/- 0.03 kcal/mol, in good agreement with previous results. In D2O the diffusion coefficient is (3.88 +/- 0.03) x 10(-5) cm2/s at 298 K and has approximately the same activation energy (4.69 +/- 0.04 kcal/mol). In comparison with classical ions, the electron diffusion has a higher activation energy, a more linear Arrhenius plot, and a slightly larger H2O/D2O isotope effect. We suggest that these differences can be explained in terms of the essentially instantaneous adiabatic response of electrons to solvent librational motions coupled with the fast dielectric relaxation of water. The electron mobility in simple alcohols is apparently not enhanced because alcohol molecules cannot respond quickly enough to high-frequency distortions of the electron charge distribution.