We present heat kernel estimates for Schrödinger operators Δ + W on weighted Riemannian manifolds. We study manifolds on which Brownian motion is recurrent; this offers some interesting technical obstacles in comparison to the transient case. Our operators feature potentials W that decay to zero at infinity, and may be critical or subcritical. In this setting we give matching upper and lower bounds for the heat kernel of Schrödinger operators. This is joint work with Laurent Saloff-Coste.