We report on spectroscopic imaging observations of the nearby ( z =0.022 ) galaxy cluster 3C 129 performed with the ACIS detector on board of the Chandra X-ray observatory . Applying a deprojection analysis which fully takes into account the spatially resolved X-ray energy spectra we investigate the radial variation of temperature and particle density of the Intracluster Medium ( ICM ) . While earlier data indicated a weak cooling flow and a cool cluster core , the Chandra data suggests that the core is hotter than the rest of the cluster : at the center we infer 7.9 ^ { +4.4 } _ { -2.4 } keV while the mean temperature of all the other ICM shells is 5.1 \pm 0.3 keV ( all errors on 90 % confidence level ) . Based on the radial entropy profile we discuss the evidence for shock heating of the ICM at the cluster center . We discuss the possibility to use imaging spectroscopy data of more regular clusters to extract maps of the gravitational dark matter potential .