  We present the first examples of cosmological solutions to four-dimensional
heterotic models which include an evolving bundle modulus. The particular
bundle modulus we consider corresponds to the width of a gauge five brane. As
such our solutions can be used to describe the evolution in one of these models
after a small instanton transition. We find that certain properties are generic
to these solutions, regardless of initial conditions. This enables us to make
some definite statements about the dynamics subsequent to a small instanton
transition despite the fact that we cannot microscopically describe the process
itself. We also show that an effective description of the small instanton
transition by a continuous matching of fields and their first derivatives is
precluded by the form of the respective low-energy theories before and after
the transition.
