  We perform a numerical study of the phase transitions in three-dimensional
Z(N) lattice gauge theories at finite temperature for N>4. Using the dual
formulation of the models and a cluster algorithm we locate the position of the
critical points and study the critical behavior across both phase transitions
in details. In particular, we determine various critical indices, compute the
average action and the specific heat. Our results are consistent with the two
transitions being of infinite order. Furthermore, they belong to the
universality class of two-dimensional Z(N) vector spin models.
