  A thermal QCD Finite Energy Sum Rule (FESR) is used to obtain the temperature
dependence of the axial-vector coupling of the nucleon, $g_{A}(T)$. We find
that $g_{A}(T)$ is essentially independent of $T$, in the very wide range $0
\leq T \leq 0.9 T_{c}$, where $T_{c}$ is the critical temperature. While
$g_{A}$ at T=0 is $q^{2}$-independent, it develops a $q^{2}$ dependence at
finite temperature. We then obtain the mean square radius associated with
$g_{A}$ and find that it diverges at $T=T_{c}$, thus signalling quark
deconfinement. As a byproduct, we study the temperature dependence of the
Goldberger-Treiman relation.
