Classical assessments of temperature trends are based on the analysis of a small number of time series. Considering trend to be only smooth changes of the mean value of a stochastic process through time is limiting, because it does not provide a mechanism to study changes of the mean that could also occur over space. Thus, in studies of climate there is a substantial interest in being able to jointly characterize temperature trends over time and space. In this article we build wavelet-based space-time hierarchical Bayesian models that can be used to simultaneously model trend, seasonality, and error, allowing for the possibility that the error process may exhibit space-time long-range dependence. We demonstrate how these statistical models can be used to assess the significance of trend over time and space. We motivate and apply our methods to the analysis of space-time temperature trends, based on data collected in the last five decades from central Sweden.