Diploma Thesis from the year 2006 in the subject Astronomy, grade: 1,3, LMU Munich (Max Planck Institut fuer Extraterrestrische Physik), language: English, abstract: We aim to analyze the most recent and deepest observation of M87 with the XMM-Newton X-ray telescope, in order to further understand the substructure and heavy element abundance profiles in the gas halo. The first and most important step in this direction is to understand the temperature distribution, from which entropy and pressure maps can be generated which are the best indications of existing substructure and especially shocks and cavities due to the interaction between the central supermassive black hole and the surrounding medium. A good understanding of the temperature maps is also needed for detailed analysis of the distribution of heavier elements produced by supernovae and mixed into in the ICM, since most emission lines are strongly temperature-dependent. We present and compare in this work two independent methods for determining the temperature profile in M87 and their results.