For the classical heat equation, many methods have been developed to derive the estimates of the heat kernel. In this talk, we consider the heat kernel H(y,t;x,l) of the time-dependent heat equation with Laplacian evolving along with a complete solution of the Ricci flow. Following a method of E.B. Daives, we first prove a double integral estimate for H(y,t;x,l). Then cooperating with a parabolic mean value inequality, we derive a Gaussian upper bound of H(y,t;x,l). Finally, by using a method of P. Li, L.-F. Tam and J. Wang, a Guassian lower bound of H(y,t;x,l) is obtained from the upper bound and certain gradient estimate.