If the Joule Thomson coefficient is negative then the forces between molecules
are repulsive (at that temperature and pressure). Therefore, allowing the
molecules to become farther apart from one another releases the energy that
was required to push them together and this increases the kinetic energy
of the system and thus the temperature. Thus, these two effects, expansion
and the negative Joule Thomson coefficient would be in opposite directions.
It is not clear if the temperature would increase or decrease.