Sensible heat storage unit is composed of a number of rectangular cross sectioned channels for the flowing fluid, connected in parallel and separated by the heat storage material. In the present analysis all parameters that affect the transient response of the thermal storage unit such as, the heat capacity, the velocity gradients and the transversal temperature variation of the heating fluid as well as axial variation of the heat transfer coefficient are considered. The governing equations are written for the temperature, vorticity and stream function in the fluid along with the heat conduction equation through the storage material. The equations have been nondimensionalized and solved with the aid of finite difference method for various values of the parameters affecting the heat storage process. Furthermore, comparison between the results obtained in this work and those obtained from the simpler models is also presented and it was found an agreement with an acceptable limits of error (7%).