The temporal development of thermal disturbances in the fluid layer heated isothermally from below is investigated, based on propagation theory. This theory is examined by using scaling. To examine the behavior of thermal instability the mean-field approximation is employed and resulting equations are solved by Galerkin method. The stability criteria to mark the onset of convective instability are newly suggested as the intersection point of the growth rate of averaged temperature with that of its fluctuation. The resulting critical time is close to that derived from propagation theory. By considering the nonlinear effects, the characteristic times to represent the detection time of manifest convection and also to exhibit the minimum Nusselt number are discussed.