  SGR 1627-41 was discovered in 1998 after a single active episode which 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 which is
followed by a sharp (factor of ten) 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 (N_H=9.0(7)x10^(22) cm^(-2)); the
spectral index, however, varies dramatically between 2.2-3.8 spanning the
entire range for all known SGR 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.
