To study the effect of slow heat conduction during phase separation, w
e discuss the relaxation properties of an O(N) symmetric model with ph
ase field type dynamics, where a nonconserved order parameter field co
uples bilinearly to a diffusive field. In the limit N --> infinity we
obtain an exact solution. The analysis reveals three different types o
f growth regimes and a very rich dynamical behavior. Finally the conne
ction with the Mullins-Sekerka instability is expounded.