In this work, we develop and study nongaussian models for processes that vary continuously in space and time. The main goal is to consider heavy tailed processes that can accommodate both aberrant observations and clustered regions with larger observational variability. These situations are quite common in meteorological applications where outliers are associated with severe weather events such as tornados and hurricanes. In this context, the idea of scale mixing a gaussian process as proposed in Palacios and Steel (JASA, 2006) is extended and the properties of the resulting process are discussed. The model is very flexible and it is able to capture variability across time that differs according to spatial locations and variability across space that differs in time. This is illustrated by an application to maximum temperature data in the Spanish Basque Country. The model allows for prediction in space-time since we can easily predict the mixing process and conditional on the latter the finite dimensional distributions are gaussian. The predictive ability is measured through proper scoring rules such as log predictive scores and interval scores. In addition, we explore the performance of the proposed model under departures from gaussianity in a simulated study where data sets were contaminated by outliers in several ways; overall, the nongaussian models recover the covariance structure well whereas the covariance structure estimated by the gaussian model is very influenced by the contamination.