Summary. Climate change may lead to changes in several aspects of the distribution of climate variables, including changes in the mean, increased variability and severity of extreme events. We propose the use of spatiotemporal quantile regression as a flexible and interpretable method for simultaneously detecting changes in several features of the distribution of climate variables. The spatiotemporal quantile regression model assumes that each quantile level changes linearly in time, permitting straightforward inference on the time trend for each quantile level. Unlike classical quantile regression which uses model-free methods to analyse a single quantile or several quantiles separately, we take a model-based approach which jointly models all quantiles, and thus the entire response distribution. In the spatiotemporal quantile regression model, each spatial location has its own quantile function that evolves over time, and the quantile functions are smoothed spatially by using Gaussian process priors. We propose a basis expansion for the quantile function that permits a closed form for the likelihood and allows for residual correlation modelling via a Gaussian spatial copula. We illustrate the methods by using temperature data for the south-east USA from the years 1931–2009. For these data, borrowing information across space identifies more significant time trends than classical non-spatial quantile regression. We find a decreasing time trend for much of the spatial domain for monthly mean and maximum temperatures. For the lower quantiles of monthly minimum temperature, we find a decrease in Georgia and Florida, and an increase in Virginia and the Carolinas.