A new technique for time series analysis (Tomé and Miranda 2004) is here extended and applied to the analysis of global gridded temperature data from NASA/GISS and from the NCEP/NCAR reanalysis. The method performs an objective fit of data by simple broken lines, where the number and location of the line breakpoints are jointly optimized subject to given constrains. When applied to a single time series, the method can be used as a versatile tool for low frequency variability analysis, offering in particular a very simple analysis of observed partial trends of mean global temperature quite similar to the results of Karl et al (2000). Here we show that the method can also be used for the study of the spatial structure of the partial trends of local temperature, allowing for the computation of a new spatially distributed climate parameter: the breakpoints of change in the local temperature tendencies. Comparisons between the two different datasets show that while the large scale structures are robust, indicating recent warming in most of the World and some hints for large warming rates in important areas such as Greenland and NE America, there are also important local differences that may be signatures of problems in either of the two data assimilation procedures.