  In this letter we report on a numerical investigation of the Aoki phase in
the case of finite temperature which continues our former study at zero
temperature. We have performed simulations with Wilson fermions at $\beta=4.6$
using lattices with temporal extension $N_{\tau}=4$. In contrast to the zero
temperature case, the existence of an Aoki phase can be confirmed for a small
range in $\kappa$ at $\beta=4.6$, however, shifted slightly to lower $\kappa$.
Despite fine-tuning $\kappa$ we could not separate the thermal transition line
from the Aoki phase.
