  We find a Gaussian off-diagonal heat kernel estimate for uniformly elliptic
operators with measurable coefficients acting on regions
$\Omega\subseteq\real^N$, where the order $2m$ of the operator satisfies
$N<2m$. The estimate is expressed using certain Riemannian-type metrics, and a
geometrical result is established allowing conversion of the estimate into
terms of the usual Riemannian metric on $\Omega$. Work of Barbatis is applied
to find the best constant in this expression.
