Indeed, there is a strong temperature dependence. If we are to speak about the normal hydrogenated water (not the heavy water) the main source of relaxation arises from the dipole-dipole interactions of protons with: 1) each other 2) protons from other molecules. In water the distance between the protons is relatively small and thus a solid water creates even a Pake-powder pattern, with splitting ~ 30 kHz. Other molecules induce only a broadening of the solid spectrum. Hence the relaxation will be governed by the intramolecular dipolar interaction with D~30kHz, T^(-1) ~ D^(2) This interaction is modulated mainly by the mobility of the water molecules: even in liquid water these are quasi-isotropic jumps of the O-H bond orientation over tetrahedral lattice. In H2O these jumps have the activation barrier of ~ 13 kJ/mol. Thus the temperature dependence will be quite pronounced already. But the situation is even more difficult as at high temperatures the signs of formation of a 5-molecules complex begin to influence the relaxation. This process actually occurs in liquid water and it is characterized by the activation barrier of ~ 40-50 kJ/mol. So it affects the spin relaxation only at high temperatures (above 70 C if i recall correctly) If you are interested in the subject: the very first papers are the seria of nice works by Hindman and co-authors. It is pretty old already, and purely liquid NMR. In 1889 Wittebort and co-authors published a very nice solid-state 1H and 2H NMR paper on water dynamics in ice, in which experimental evidences and spectra simulations are given. The latter study correlates with Hindman findings. Another hint about water -since the main relaxation mechanism is the water microscopic mobility, one could expect that the temperature dependence of the spin relaxation will be correlated with the temperature dependence of the viscosity. The subject is nicely shown in Hindman papers, it is indeed impressive. To obtain the curve of the spin-lattice relaxation TD one just have to scale by a constant numerical factor the TD of the viscosity.

If you wish a formula the Hindman paper is for you - there the TD is fitted by a simple two-lorenzian approximation with two characteristic Arrhenius correlation times, one for the solo jumping and another for the mobility in a complex.

Hope it helped =)