  In the previous papers in this series, we found that radiative torques can
play a major role in the alignment of grains with the interstellar magnetic
field. Since the radiative torques can drive the grains to suprathermal
rotational speeds, in previous work we made the simplifying assumption that the
grain principal axis of greatest moment of inertia is always parallel to the
grain angular momentum. This enabled us to describe many of the features of the
grain dynamics. However, this assumption fails when the grains enter periods of
thermal rotation, which occur naturally in the radiative torque alignment
scenario. In the present paper, we relax this assumption and explore the
consequences for the grain dynamics. We develop a treatment to follow the grain
dynamics including thermal fluctuations and ``thermal flipping'', and show
results for one illustrative example. By comparing with a treatment without
thermal fluctuations, we see that inclusion of thermal fluctuations can lead to
qualitative changes in the grain dynamics. In a future installment in this
series, we will use the more complete dynamical treatment developed here to
perform a systematic study of grain alignment by radiative torques.
