We study singularities of solutions of the heat
equation, that are not necessarily isolated but occur only in a single
characteristic hyperplane. We prove a decomposition theorem for certain
solutions on

,
for a suitable open
set

*D*, with singularities at a compact subset

*K* of

,
in terms of Gauss-Weierstrass integrals. We use this to prove a
representation theorem for certain solutions on

*D*_{+}, with
singularities at

*K*, as the sums of potentials and Dirichlet
solutions. We also give conditions under which

*K* is removable for
solutions on

.