  We prove two stability results for the scale invariant solutions of the
nonlinear heat equation $\partial_t u=\Delta u - |u|^{p-1}u$ with
$1<p<1+{2\over n}$, $n$ being the spatial dimension. The first result is that a
small perturbation of a scale invariant solution vanishes as
$t\rightarrow\infty$. The second result is global, with a positivity condition
on the initial data.
