  We use methods of quantum field theory in toroidal topologies to study the
$N$-component $D$-dimensional massive Gross-Neveu model, at zero and finite
temperature, with compactified spatial coordinates. We discuss the behavior of
the large-$N$ coupling constant ($g$), investigating its dependence on the
compactification length ($L$) and the temperature ($T$). For all values of the
fixed coupling constant ($\lambda$), we find an asymptotic-freedom type of
behavior, with $g\to 0$ as $L\to 0$ and/or $T\to \infty$. At T=0, and for
$\lambda \geq \lambda_{c}^{(D)}$ (the strong coupling regime), we show that,
starting in the region of asymptotic freedom and increasing $L$, a divergence
of $g$ appears at a finite value of $L$, signaling the existence of a phase
transition with the system getting spatially confined. Such a spatial
confinement is destroyed by raising the temperature. The confining length,
$L_{c}^{(D)}$, and the deconfining temperature, $T_{d}^{(D)}$, are determined
as functions of $\lambda$ and the mass ($m$) of the fermions, in the case of
$D=2,3,4$. Taking $m$ as the constituent quark mass ($\approx 350\: MeV$), the
results obtained are of the same order of magnitude as the diameter ($\approx
1.7 fm$) and the estimated deconfining temperature ($\approx 200\: MeV$) of
hadrons.
