  We discuss the heat content asymptotics associated with the heat flow out of
a smooth compact manifold in a larger compact Riemannian manifold. Although
there are no boundary conditions, the corresponding heat content asymptotics
involve terms localized on the boundary. The classical pseudo-differential
calculus is used to establish the existence of the complete asymptotic series
and methods of invariance theory are used to determine the first few terms in
the asymptotic series in terms of geometric data. The operator driving the heat
process is assumed to be an operator of Laplace type.
