Climate change is the result of complex interactions between a wide array of climatic variables. Over a long period of time, climatic patterns can shift, possibly multiple times. Abrupt shifts that occur over a relatively short period of time are known as change points. During these intervals, different climatic variables may undergo dramatic shifts posing serious consequences for many biological and physical systems. In this paper, we discuss a Bayesian algorithm for detecting the location of change points in time series data. In particular, we utilize our method to analyse five different global surface temperature anomaly data sets, as well as temperature records associated with land, ocean, and different zonal bands in an attempt to identify common features of these data sets. Change points in the five global records were detected between 1902-1917, 1936-1945, and 1963-1976, but do these change points also manifest themselves across other parts of the globe? Our analysis indicates that the timing of change points is consistent from one record to the next, but not all change points appear in all records. In particular, there were more change points in the ocean than on land, and also more change points in southern latitudes than in northern latitudes.