  The evolution of binaries consisting of evolved main sequence stars (1 <
M_d/Msun < 3.5) with white dwarf companions (0.7 < M_wd/Msun < 1.2) is
investigated through the thermal mass transfer phase. Taking into account the
stabilizing effect of a strong, optically thick wind from the accreting white
dwarf surface, we have explored the formation of several evolutionary groups of
systems for progenitors with initial orbital periods of 1 and 2 days. The
numerical results show that CO white dwarfs can accrete sufficient mass to
evolve to a Type Ia supernova and ONeMg white dwarfs can be built up to undergo
accretion induced collapse for donors more massive than about 2 Msun. For
donors less massive than ~2 Msun the system can evolve to form a He and CO or
ONeMg white dwarf pair. In addition, sufficient helium can be accumulated (~0.1
Msun) in systems characterized by 1.6 < M_d/Msun < 1.9 and 0.8 < M_wd/Msun < 1
such that sub Chandrasekhar mass models for Type Ia supernovae, involving off
center helium ignition, are possible for progenitor systems evolving via the
Case A mass transfer phase. For systems characterized by mass ratios > 3 the
system likely merges as a result of the occurrence of a delayed dynamical mass
transfer instability. A semi-analytical model is developed to delineate these
phases which can be easily incorporated in population synthesis studies of
these systems.
