  We study the extreme point process associated to the off-diagonal components
in the matrix representation of the Gaussian $\beta$-Ensemble and prove its
convergence to Poisson point process as $n\to +\infty$ when the inverse
temperature $\beta$ scales with $n$ and tends to $0$. We consider two main high
temperature regimes: $\displaystyle{\beta\ll \frac{1}{n}}$ and
$\displaystyle{n\beta= 2\gamma \geq 0}$. The normalizing sequences are
explicitly given in each cases. As a consequence, we estimate the first order
asymptotic of the largest eigenvalue of the Gaussian $\beta$-Ensemble.
