- SGR 1627-41 was discovered in 1998 after a single active episode that lasted ~6 weeks. We report here our monitoring results of the decay trend of the persistent X-ray luminosity of the source during the last 5 years. We find an initial temporal power-law decay with index 0.47, reaching a plateau that is followed by a sharp (factor of 10) flux decline ~800 days after the source activation. The source spectrum is best described during the entire period by a single power law with high absorption [NH = 9.0(7) × 1022 cm-2]; the spectral index, however, varies dramatically between 2.2 and 3.8 spanning the entire range for all known soft gamma repeater sources. We discuss the cooling behavior of the neutron star assuming a deep crustal heating initiated by the burst activity of the source during 1998.