The partition function, PI of water is calculated by explicit summation of similar to 200 000 vibration-rotation levels computed using variational nuclear motion calculations. Temperatures up to 6000 K are studied. Estimates are obtained for the heat capacity (C-p), the Gibbs enthalpy factor (gef), the Helmholtz function (hcf), and the entropy (S) of gas-phase water as a function of temperature. To get converged results at higher temperatures it is necessary to augment the accurate list of energy levels. This is done using estimates for all the vibrational band origins to dissociation and rotational levels calculated using Pade approximants. The widely used method of computing the internal partition function as the product of vibrational and rotational partition functions is tested and found to overestimate the partition function by up to 10%. The present estimates of Q(T), C-p(T). gef( T), hcf(T), and S(T) are probably the most accurate available for water at temperatures, T, above 2000 K. Errors, as a function of temperature, are estimated in each case.