  We prove Gaussian type bounds for the fundamental solution of the conjugate
heat equation evolving under the Ricci flow. As a consequence, for dimension 4
and higher, we show that the backward limit of type I $\kappa$-solutions of the
Ricci flow must be a non-flat gradient shrinking Ricci soliton. This extends
Perelman's previous result on backward limits of $\kappa$-solutions in
dimension 3, in which case that the curvature operator is nonnegative (follows
from Hamilton-Ivey curvature pinching estimate). The Gaussian bounds that we
obtain on the fundamental solution of the conjugate heat equation under
evolving metric might be of independent interest.
