The onset of buoyancy-driven convection in an initially isothermal, quiescent fluid layer heated from below with a constant heating rate is analyzed by the propagation theory. Here the dimensionless critical time tau(c) to mark the onset of convective motion is presented as a function of the Rayleigh number Ra-phi and the Prandtl number Pr. The present stability analysis predicts that for a given large Ra-phi, tau(c) decreases with increasing Pr and it is independent of the conditions of the upper boundary. For deep-pool systems, the deviation of the temperature profile from conduction state occurs starting from a certain time tau(o)congruent to tau c. The present predictions are compared with other models and existing experimental results in the whole time domain. (c) 2005 Elsevier Ltd. All rights reserved.