Using CHANDRA, we investigate the spatial temperature distribution of the intracluster medium (ICM) within 700 kpc of the center of the massive merging cluster MACSJ0717.5+3745 at z=0.55. Combining the X-ray evidence with information about the distribution and velocities of the cluster galaxies near the core provides us with a snapshot of the three-dimensional geometry and dynamics of one of the most complex cluster studied to date. We find MACSJ0717.5+3745 to be an active triple merger with ICM temperatures exceeding 20 keV. Although radial velocity information and X-ray/optical offsets indicate that all three mergers proceed along distinctly different directions, the partial alignment of the merger axes points to a common origin in the large-scale filament south-east of the cluster core. Clear decrements in the ICM temperature observed near two of these subclusters identify the respective X-ray surface brightness peaks as remnants of cool cores; the compactness and low temperature of 5.7 keV of one of these features suggest that the respective merger, a high-velocity collision at 3,000 km/s, is still in its very early stages. Looking beyond the triple merger, we find the large-scale filament to not only provide a spatial as well as temporal arrow for the interpretation of the dynamics of the merger events near the cluster core; we also find tantalizing, if circumstantial, evidence for direct, large-scale heating of the ICM by contiguous infall of low-density gas from the filament.