One of the most important factors of controlling the properties of the above mentioned systems is hydrostatic pressure and temperature. The effect of the hydrostatic pressure and temperature on diamagnetic susceptibility and binding energy of a center hydrogenic donor impurity has been theoretically investigated in the framework of the effective mass approximation. We describe the quantum confinement by an infinite deep potential. The results for a cylindrical Inhomogeneous quantum dots made out of [CdS (Core) / HgS (Well) / CdS (Shell)] show that (i) when the hydrostatic pressure increase, the diamagnetic susceptibility decreases and the binding energy increases. (ii) The diamagnetic susceptibility increases with the temperature.