The approximation known as Frozen Convection has been widely used in the context of stellar oscillations due to the lack of a Time Dependent Convection theory. This approximation supposes to neglect the interaction between convection and oscillations and there are different ways to do it. The choice can affect theoretical predictions concerning the non-adiabatic treatment of the stellar oscillations. In fact, fictitious excitation or damping of the pulsation modes can be produced depending on the approximation used.