A theoretical study is carried out for the cavity cooling of a $Lambda$-type three level atom in a high-finesse optical cavity with a weakly driven field. Analytical expressions for the friction, diffusion coefficients and the equilibrium temperature
s are obtained by using the Heisenberg equations, then they are calculated numerically and shown graphically as a function of controlling parameters. For a suitable choice of these parameters, the dynamics of the cavity field interaction with the $Lambda$-type three-level atom introduces a sisyphus cooling mechanism yielding lower temperatures below the Doppler limit and allowing larger cooling rate, avoiding the problems induced by spontaneous emission.
