We present a detailed X-ray study of the intracluster medium ( ICM ) of the nearby , cool-core galaxy cluster Abell 478 ( z = 0.088 ) , based on Chandra and XMM-Newton observations . Using a wavelet smoothing hardness analysis , we derive detailed temperature maps of A478 , revealing a surprising amount of temperature structure for an apparently well relaxed cluster . We find the broad band Chandra spectral fits yield temperatures which are significantly hotter than those obtained with XMM-Newton , but the Fe ionization temperature shows good agreement . We show that the temperature discrepancy is slightly reduced when comparing spectra from regions selected to enclose nearly isothermal gas . However , by simulating multi-temperature spectra and fitting them with a single temperature model , we find no significant difference between Chandra and XMM-Newton , indicating that non-isothermality can not fully explain the discrepancy . We have discovered four hot spots located between 30–50 kpc from the cluster center , where the gas temperature is roughly a factor of 2 higher than in the surrounding material . We estimate the combined excess thermal energy present in these hot spots to be ( 3 \pm 1 ) \times 10 ^ { 59 } erg . The location of and amount of excess energy present in the hot spots are suggestive of a common origin within the cluster core , which hosts an active galactic nucleus . This cluster also possesses a pair of X-ray cavities coincident with weak radio lobes , as reported in a previous analysis , with an associated energy of less than 10 % of the thermal excess in the hot spots . The presence of these hot spots could indicate strong-shock heating of the intracluster medium from the central radio source – one of the first such detections in a cool core cluster . Using the high resolution of Chandra , we probe the mass distribution in the core and find it to be characterized by a logarithmic slope of -0.35 \pm 0.22 , which is significantly flatter than an NFW cusp of -1 and consistent with recent strong lensing results for a number of clusters .