  We continue previous investigations of the (inhomogeneous) phase structure of
the Gross-Neveu model in a noninteger number of spatial dimensions ($1 \leq d <
3$) in the limit of an infinite number of fermion species ($N \to \infty$) at
(non)zero chemical potential $\mu$. In this work, we extend the analysis from
zero to nonzero temperature $T$.
  The phase diagram of the Gross-Neveu model in $1 \leq d < 3$ spatial
dimensions is well known under the assumption of spatially homogeneous
condensation with both a symmetry broken and a symmetric phase present for all
spatial dimensions. In $d = 1$ one additionally finds an inhomogeneous phase,
where the order parameter, the condensate, is varying in space. Similarly,
phases of spatially varying condensates are also found in the Gross-Neveu model
in $d = 2$ and $d = 3$, as long as the theory is not fully renormalized, i.e.,
in the presence of a regulator. For $d = 2$, one observes that the
inhomogeneous phase vanishes, when the regulator is properly removed (which is
not possible for $d = 3$ without introducing additional parameters).
  In the present work, we use the stability analysis of the symmetric phase to
study the presence (for $1 \leq d < 2$) and absence (for $2 \leq d < 3$) of
these inhomogeneous phases and the related moat regimes in the fully
renormalized Gross-Neveu model in the $\mu, T$-plane. We also discuss the
relation between "the number of spatial dimensions" and "studying the model
with a finite regulator" as well as the possible consequences for the limit $d
\to 3$.
