  In this note, we give a new proof for Perelman's scalar curvature and
diameter estimates for the K\"ahler-Ricci flow on Fano manifolds. The proof
relies on a new Harnack estimate for a special family of functions in
space-time. Our new approach initiates the work in \cite{JST23a} for general
finite time solutions of the K\"ahler-Ricci flow.
