There is a need for accurate data on the rate constants of many reactions involved in the radiolysis of water at high temperature and pressure, to model aqueous chemistry in the heat transport systems of water-cooled nuclear reactors. Given the absence of direct experimental data, it is usual to extrapolate rate constants from lower temperature measurements. However, recent studies of muonium kinetics show that rate constants go through a maximum and fall with temperature under near critical and supercritical conditions. This behavior can be explained by the cage effect, in particular the number of collisions between a pair of reactants over the duration of their encounter. The model developed for reactions of muonium is equally valid for fast reactions in the radiolysis of water. It is used here to estimate the rate constants of near diffusion-controlled reactions of hydroxyl radicals in sub- and supercritical water. The results show significant differences from literature values commonly used to model aqueous radiation chemistry in nuclear reactors. In view of this, it is recommended that the predictions of earlier models be reconsidered.