We report on the quiescent state of the Soft Gamma Repeater SGR 0501+4516 observed by XMM-Newton on 2009 August 30. The source exhibits an absorbed flux ~75 times lower than that measured at the peak of the 2008 outburst, and a rather soft spectrum, with the same value of the blackbody temperature observed with ROSAT back in 1992. This new observation is put into the context of all existing X-ray data since its discovery in August 2008, allowing us to complete the study of the timing and spectral evolution of the source from outburst until its quiescent state. The set of deep XMM-Newton observations performed during the few-years timescale of its outburst allows us to monitor the spectral characteristics of this magnetar as a function of its rotational period, and their evolution along these years. After the first ~10 days, the initially hot and bright surface spot progressively cooled down during the decay. We discuss the behaviour of this magnetar in the context of its simulated secular evolution, inferring a plausible dipolar field at birth of 3x10^14 G, and a current (magneto-thermal) age of ~10 kyr.
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