[en] The most intense pulsed muon beam will be generated by a 3-GeV 333-microA proton beam on a muon target made of 20-mm thick isotropic graphite (IG-430) in J-PARC/MUSE (Muon Science Establishment). The energy deposited by a 1-MW proton beam is estimated to be 3.9 kW on the muon target. The first muon beam was successfully generated on September 26th, 2008. Gradually upgrading the beam intensity, continuous 300-kW proton beam operation was started in January of 2013. The temperatures of the principle components have been measured and recorded through thermocouples and a control system. The lifetime of the muon target is determined by a proton-irradiation damage of the graphite. Even in the 300-kW operation to July of 2013, the radiation damage was anticipated to surpass the lifetime. Therefore, the position of the proton beam has been moved to eight surrounding positions every three weeks to distribute the radiation damage uniformly to a wider area. The position-control is named EXILE operation. The variation of the temperatures at the muon target has been monitored. In this report, the status of proton beam operation and the lifetime extension of the muon target will be described. (author)