  One promising method to test progenitor models for Type Ia supernovae is to
identify surviving companion stars in historical supernova remnants. A
surviving companion will have been strongly affected by its interaction with
the supernova ejecta. Here we systematically explore the evolution and
appearance of a typical companion star that has been stripped and heated by the
supernova interaction during the post-impact re-equilibration phase. We show
that, depending on the amount of heating and the amount of mass stripped by the
impact or the previous binary mass transfer, such a star may be significantly
overluminous or underluminous 10^3 - 10^4 yr after the supernova relative to
its pre-supernova luminosity (by up to two orders of magnitude) and discuss the
implications of these results for the strategies to be employed in searches for
such companions.
