Because of its intrinsic interest and its many applications in various areas of mathematics, the heat diffusion equation on manifolds has been studied intensively. In particular, during the past 30 years many authors attacked the problem of describing the global behavior of the heat diffusion kernel. The aim of this paper is to prove satisfactory estimates for the heat kernel on complete manifolds with finitely many ends. It is well established that the long time behavior of the heat kernel reflects, in some way, the large scale geometry of the manifold. Still, the number of situations for which satisfactory upper and lower global bounds are known is very limited.