Almost all archaeological ceramics undergo slow, progressive rehydroxylation by chemical combination with environmental water. The reaction is accompanied by an expansion, and also by the small but measurable mass gain that provides the basis for the RHX dating method. The rate of the RHX reaction increases with increasing temperature. Here we describe comprehensively the effects of temperature on the RHX process in relation to the dating methodology. We deal in turn with the kinetic model of the RHX reaction, the temperature dependence of the RHX rate, and the influence of varying environmental temperature on the RHX mass gain. We define an effective lifetime temperature and show how this is calculated from an estimated lifetime temperature history. Historical meteorological temperature data are used to estimate the lifetime temperature history, and this can be adjusted for long-term climate variation. We show also how to allow for the effects of burial in archaeological sites on the temperature history. Finally we describe how the uncertainties in estimates of RHX age depend on the estimates of temperature history and effective lifetime temperature.