We use temperature-dependent ultrafast infrared spectroscopy of dilute HOD in H(2)O to study the picosecond reorganization of the hydrogen bond network of liquid water. Temperature-dependent two-dimensional infrared (2D IR), pump-probe, and linear absorption measurements are self-consistently analyzed with a response function formalism that includes the effects of spectral diffusion, population lifetime, reorientational motion, and nonequilibrium heating of the local environment upon vibrational relaxation. Over the range 278-345 K, we find the time scales of spectral diffusion and reorientational relaxation decrease from approximately 2.4 to 0.7 ps and 4.6 to 1.2 ps, respectively, which corresponds to barrier heights of 3.4 and 3.7 kcal/mol, respectively. We compare the temperature dependence of the time scales to a number of measures of structural relaxation and find similar effective activation barrier heights and slightly non-Arrhenius behavior, which suggests that the reaction coordinate for the hydrogen bond rearrangement in water is collective. Frequency and orientational correlation functions computed from molecular dynamics (MD) simulations over the same temperature range support our interpretations. Finally, we find the lifetime of the OD stretch is nearly the same from 278 K to room temperature and then increases as the temperature is increased to 345 K.