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 D+ = D ∩ (Rn × ]0. ∞[), for a suitable open set D, with singularities at compact subset K of Rn × {0}, 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 D∖K.
