  We consider the asymptotic expansion of the heat kernel of a generalized
Laplacian for $t\to 0^+$ and characterize the coefficients $a_k$ of this
expansion by a natural intertwining property. In particular we will give a
closed formula for the infinite order jet of these coefficients on the diagonal
in terms of the local expressions of the powers of the given generalized
Laplacian in normal coordinates.
