  Let $D$ be a bounded, connected, open set in Euclidean space $\mathbb{R}^{2}$
with polygonal boundary. Suppose $D$ has initial temperature $1$ and the
complement of $D$ has initial temperature $0$. We obtain the asymptotic
behaviour of the heat content of $D$ as time $t \downarrow 0$. We then apply
this result to compute the heat content of a particular fractal polyhedron as
$t \downarrow 0$.
