THE MAIN GOAL OF OUR XMM-NEWTON OBSERVATION OF MAXIJ0556{332 IS TO STUDY THE INTERIOR PROPERTIES OF THE NEUTRON STAR IN THIS SYSTEM. UNDERSTANDING THE BEHAVIOR OF MATTER UNDER THE EXTREME CONDITIONS IN NEUTRON STARS REMAINS ONE OF THE CORNERSTONES OF HIGH-ENERGY ASTROPHYSICS. IN THE PAST DECADE THE STUDY OF COOLING NEUTRON STARS IN TRANSIENTLY ACCRETING SYSTEMS HAS EMERGED AS A NEW APPROACH TO UNDERSTANDING THE STRUCTURE OF NEUTRON STARS. ONE OF THE NEWEST MEMBERS OF THE SAMPLE OF COOLING NEUTRON STARS IS MAXIJ0556{332 AN X-RAY TRANSIENT THAT HAD BEEN IN OUTBURST FOR _16 MONTHS WHEN IT RETURNED TO QUIESCENCE IN MAY 2012. XMM-NEWTON AND CHANDRA OBSERVATIONS MADE DURING THE _RST _1230 DAYS OF QUIESCENCE REVEALED THAT THE NEUTRON STAR IN MAXIJ0556{332 IS EXCEPTIONALLY HOT COMPARED TO OTHER NEUTRON STARS THAT HAVE BEEN HEATED BY ACCRETION. OUR NEW XMM-NEWTON OBSERVATION WILL EXTEND OUR COVERAGE TO _1750 DAYS INTO QUIESCENCE. WE WILL USE IMPROVED SPECTRAL MODELS FOR THE X-RAY SPECTRA THAT ALLOW FOR A WIDER RANGE OF NEUTRON-STAR PARAMETERS AND THEORETICAL THERMAL EVOLUTION MODELS FOR COOLING CURVES.