We obtain a master equation for a parametrically driven optomechanical cavity. We use a more correct dissipation model that accounts for the modification of the quasi-energy spectrum caused by the driving. When the natural frequency of the mechanical object oscillates periodically around its mean value, the master equation with the improved dissipation model is expressed using Floquet operators. We apply the corresponding master equation to model the laser cooling of the mechanical object. Using an adiabatic approximation, an analytical expression for the number of excitations of the mechanical oscillator can be obtained. We find that the number of excitations can be lower than in the non-time dependent case. Our results raise the possibility of achieving lower temperatures for the mechanical object if its natural frequency can be controlled as a function of time.