  This paper is the sequel to our study of heat kernels on Ricci shrinkers in
\cite{LW20}. In this paper, we improve many estimates in \cite{LW20} and extend
the recent progress of Bamler \cite{Bam20a}. In particular, we drop the
compactness and curvature boundedness assumptions and show that the theory of
$\IF$-convergence holds naturally on any Ricci flows induced by Ricci
shrinkers.
