  Let $\overline G$ be the wonderful compactification of a simple affine
algebraic group $G$ defined over $\mathbb C$ such that its center is trivial
and $G\not= {\rm PSL}(2,\mathbb{C})$. Take a maximal torus $T \subset G$, and
denote by $\overline T$ its closure in $\overline G$. We prove that $T$
coincides with the connected component, containing the identity element, of the
group of automorphisms of the variety $\overline T$.
