  We explicitly compute the diffeomorphism group of several types of linear
foliations (with dense leaves) on the torus $T^n$, $n\geq 2$, namely
codimension one foliations, flows, and the so-called non-quadratic foliations.
We show in particular that non-quadratic foliations are rigid, in the sense
that they do not admit transverse diffeomorphisms other than $\pm \id$ and
translations. The computation is an application of a general formula that we
prove for the diffeomorphism group of any Lie foliation with dense leaves on a
compact manifold. Our results generalize those of P. Donato and P. Iglesias for
$T^2$, P. Iglesias and G. Lachaud for codimension one foliations on $T^n$,
$n\geq 2$, and B. Herrera for transcendent foliations. The theoretical setting
of the paper is that of J. M. Souriau's diffeological spaces.
