A Bayesian hierarchical space-time model is proposed by combining information from real-time ambient AIRNow air monitoring data, and output from a computer simulation model known as the Community Multi-scale Air Quality (Eta-CMAQ) forecast model. A model validation analysis shows that the interpolated maps are more accurate than the maps based solely on the Eta-CMAQ forecast data for a two week test period. The out-of sample spatial predictions and temporal forecasts also outperform those from regression models with independent Gaussian errors. The method is fully Bayesian and is able to instantly update the map for the current hour (upon receiving monitor data for the current hour) and forecast the map for several hours ahead. In particular, the eight-hour average map which is the average of the past four hours, current hour and three hours ahead is instantly obtained at the current hour. The exact Bayesian method proposed here is preferable to more complex (possibly more accurate) models since iterative methods such as the Markov chain Monte Carlo (MCMC) are not required to obtain the fitting and forecasting results.