  The renormalization of effective potentials for the noncommutative scalar
field theory at high temperature are investigated to the two-loop
approximation. The Feynman diagrams in evaluating the effective potential may
be classified into two types: the planar diagrams and nonplanar diagrams. The
nonplanar diagrams, which depend on the parameter of noncommutativity, do not
appear in the one-loop potential. Despite their appearance in the two-loop
level, they do not have an inclination to restore the symmetry breaking in the
tree level, in contrast to the planar diagrams. This phenomenon is explained as
a consequence of the drastic reduction of the degrees of freedom in the
nonplanar diagrams when the thermal wavelength is smaller than the
noncommutativity scale. Our results show that the nonplanar two-loop
contribution to the effective potential can be neglected in comparsion with
that from the planar diagrams.
