  Interstellar dust grains are non-spherical and, in some environments,
partially aligned along the direction of the interstellar magnetic field.
Numerous alignment theories have been proposed, all of which examine the grain
rotational dynamics. In 1999, Lazarian & Draine introduced the important
concept of thermal flipping, in which internal relaxation processes induce the
grain body to flip while its angular momentum remains fixed. Through detailed
numerical simulations, we study the role of thermal flipping on the grain
dynamics during periods of relatively slow rotation, known as `crossovers', for
the special case of a spheroidal grain with a non-uniform mass distribution.
Lazarian & Draine proposed that rapid flipping during a crossover would lead to
`thermal trapping', in which a systematic torque, fixed relative to the grain
body, would time average to zero, delaying spin-up to larger rotational speeds.
We find that the time-averaged systematic torque is not zero during the
crossover and that thermal trapping is not prevalent. As an application, we
examine whether the classic Davis-Greenstein alignment mechanism is viable, for
grains residing in the cold neutral medium and lacking superparamagnetic
inclusions. We find that Davis-Greenstein alignment is not hindered by thermal
trapping, but argue that it is, nevertheless, too inefficient to yield the
alignment of large grains responsible for optical and infrared starlight
polarization. Davis-Greenstein alignment of small grains could potentially
contribute to the observed ultraviolet polarization. The theoretical and
computational tools developed here can also be applied to analyses of alignment
via radiative torques and rotational disruption of grains.
