  We present X-ray observations of the transient accretion-powered millisecond
pulsar IGR J00291+5934 during quiescence. IGR J00291+5934 is the first source
among accretion powered millisecond pulsars to show signs of a thermal
component in its quiescent spectrum. Fitting this component with a neutron star
atmosphere or a black body model we obtain soft temperatures (~64 eV and ~110
eV, respectively). As in other sources of this class a hard spectral component
is also present, comprising more than 60% of the unabsorbed 0.5-10 keV flux.
Interpreting the soft component as cooling emission from the neutron star, we
can conclude that the compact object can be spun up to milliscond periods by
accreting only <0.2 solar masses.
