  In this article we study restoration of chiral symmetry at finite temperature
for quark matter with a chiral chemical potential, $\mu_5$, by means of a
quark-meson model with vacuum fluctuations included. Vacuum fluctuations give a
divergent contribution to the vacuum energy, so the latter has to be
renormalized before computing physical quantities. The vacuum term is important
for restoration of chiral symmetry at finite temperature and $\mu_5\neq0$,
therefore we present several plausible renormalization schemes for the
ultraviolet divergences at $\mu_5\neq0$. Then we compute the critical
temperature as a function of $\mu_5$. The main result of our study is that the
choice of a renormalization scheme affects the critical temperature; among the
three renormalization schemes we investigate, there exists one in which the
critical temperature increases with $\mu_5$, a result which has not been found
before by chiral model studies and which is in qualitative agreement with
recent lattice data as well as with studies based on Schwinger-Dyson equations
and universality arguments.
