  We consider a toy model of interacting Dirac fermions in a 1+1 dimensional
space time describing the exterior of a star collapsing to a blackhole. In this
situation we give a rigorous proof of the {\em Hawking effect}, namely that
under the associated quantum evolution, an initial vacuum state will converge
when $t\to +\infty$ to a thermal state at Hawking temperature. We establish
this result both for observables falling into the blackhole along null
characteristics, and for static observables. We also consider the case of an
interaction localized near the star boundary, obtaining similar results. We
hence extend to an interacting model previous results of Bachelot and Melnyk,
obtained for free Dirac fields.
