  We first generalize a decomposition of functions on Carnot groups as linear
combinations of the Dirac delta and some of its derivatives, where the weights
are the moments of the function.
  We then use the decomposition to describe the large time behavior of
solutions of the hypoelliptic heat equation on Carnot groups. The solution is
decomposed as a weighted sum of the hypoelliptic fundamental kernel and its
derivatives, the coefficients being the moments of the initial datum.
