We present an X-ray timing and spectral analysis of the Be/X-ray binary SAX J2103.5+4545 at a time when the Be stars circumstellar disk had disappeared and thus the main reservoir of material available for accretion had extinguished. In this very low optical state, pulsed X-ray emission was detected at a level of L_X~10^{33} erg/s. This is the lowest luminosity at which pulsations have ever been detected in an accreting pulsar. The derived spin period is 351.13 s, consistent with previous observations. The source continues its overall long-term spin-up, which reduced the spin period by 7.5 s since its discovery in 1997. The X-ray emission is consistent with a purely thermal spectrum, represented by a blackbody with kT=1 keV. We discuss possible scenarios to explain the observed quiescent luminosity and conclude that the most likely mechanism is direct emission resulting from the cooling of the polar caps, heated either during the most recent outburst or via intermittent accretion in quiescence.