  We extend to the parabolic setting some of the ideas originated with Xiao
Zhong's proof in \cite{Zhong} of the H\"older regularity of $p-$harmonic
functions in the Heisenberg group $\Hn$. Given a number $p\ge 2$, in this paper
we establish the $C^{\infty}$ smoothness of weak solutions of quasilinear pde's
in $\Hn$ modelled on the equation $$\p_t u= \sum_{i=1}^{2n} X_i
\bigg((1+|\nabla_0 u|^2)^{\frac{p-2}{2}} X_i u\bigg).$$
