Max-stable processes are the natural analogues of the generalized extreme value distribution when modelling extreme events in space and time. Under suitable conditions, these processes are asymptotically justified models for maxima of independent replications of random fields, and they are also suitable for the modelling of extreme measurements over high thresholds. The paper shows how a pairwise censored likelihood can be used for consistent estimation of the extremes of space–time data under mild mixing conditions and illustrates this by fitting an extension of a model due to Schlather to hourly rainfall data. A block bootstrap procedure is used for uncertainty assessment. Estimator efficiency is considered and the choice of pairs to be included in the pairwise likelihood is discussed. The model proposed fits the data better than some natural competitors.