  Let $H$ be a norm of ${\bf R}^N$ and $H_0$ the dual norm of $H$. Denote by
$\Delta_H$ the Finsler-Laplace operator defined by
$\Delta_Hu:=\mbox{div}\,(H(\nabla u)\nabla_\xi H(\nabla u))$. In this paper we
prove that the Finsler-Laplace operator $\Delta_H$ acts as a linear operator to
$H_0$-radially symmetric smooth functions. Furthermore, we obtain an optimal
sufficient condition for the existence of the solution to the Cauchy problem
for the Finsler heat equation $$ \partial_t u=\Delta_H u,\qquad x\in{\bf
R}^N,\quad t>0, $$ where $N\ge 1$ and $\partial_t:=\partial/\partial t$.
