  We compute the finite temperature correction to the induced fermion number
for fermions coupled to a static SU(2) chiral background, using the derivative
expansion technique. At zero temperature the induced fermion number is
topological, being the winding number of the chiral background. At finite
temperature however, higher order terms in the derivative expansion give
nontopological corrections to the winding number. We use this result to show
that the standard cancellation of the fractional parts of the fermion number
inside and outside the bag in an SU(2) x SU(2) hybrid chiral bag model of the
nucleon does not occur at nonzero temperature.
