A suitable model for analyzing rainfall data needs to take into account variation in both space and time. The method of kriging is a popular approach in spatial statistics which makes predictions for spatial data. Kalman filtering using dynamic models is often used to analyze temporal data. These approaches have been combined in a classical framework termed kriged Kalman filter (KKF) model. In the combined model, the kriging predictions dictate the optimal regression surface for incorporating spatial structure and the dynamic linear model framework is used to learn about temporal factors such as trends, autoregressive components and cyclical variations. In this article we consider a full Bayesian KKF (BKKF) model for rainfall data and its MCMC implementation. The MCMC techniques provide unified estimation of spatio-temporal effects and allow optimal predictions in time and space. The methods are illustrated with two real data examples. Using many well known validation methods we highlight the advantages of the BKKF model.