  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 temperatures 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.
