  We prove a Davies type double integral estimate for the heat kernel
$H(y,t;x,l)$ under the Ricci flow. As a result, we give an affirmative answer
to a question proposed by Chow etc.. Moreover, we apply the Davies type
estimate to provide a new proof of the Gaussian upper and lower bounds of
$H(y,t;x,l)$ which were first shown by Chau-Tam-Yu.
