The dependence of the decay time constant of a thermalized neutron pulse in H2O has been calculated both as a function of buckling and of temperature for the range of temperatures between 23 C and 300 C. Fair agreement between results for two moderator models and experiment has been found for the dependence of the diffusion coefficient on temperature. For higher coefficients in the buckling expansion the agreement is poorer. A new iterative method applicable to any moderator model has been used for the solution of the eigenvalue problem. This method is suited to high-order approximations to the transport equation, a P11 approximation having been used in the present calculations. Convergence is rapid. An advantage is that the diffusion-cooled neutron fluxes are given accurately; these are presented and discussed.