  We establish an estimate for the fundamental solution of the heat equation on
a closed Riemannian manifold $M$ of dimension at least 3, evolving under the
Ricci flow. The estimate depends on some constants arising from a Sobolev
imbedding theorem. Considering the case when the scalar curvature is positive
throughout the manifold, at any time, we will obtain, as a corollary, a bound
similar to the one known for the fixed metric case.
