The extended Rayleigh-Benard problem, where an unperturbed temperature profile is nonlinear and time-dependent, was examined by linear stability theory. The unperturbed temperature profile induced by constant heat flux from below was approximated, using a bottom temperature and penetration distance. Applying this modified temperature profile to the present system, the asymptotic power-series method was developed and the onset of natural convection was analyzed. It was found that this analysis is well applied to the transient system with the Rayleigh number larger than 10⁴. It is evident that for large Prandtl numbers temperature disturbances are confined within the effective thermal depth.