The onset of convective motion in a horizontal fluid layer under constant flux heating is analyzed by the modified frozen-time analysis confining temperature disturbances within a thermal penetration distance. For this purpose a new mathematical method is introduced in detail. It is found that the present stability analysis predicts the most reliable critical conditions based on the comparisons with the published experiments and theoretical models. At _c<0.01, the stability conditions lead to Ra_c = 14.1 _c^-2 and a_c = 0.248 Ra_c^1/4 and the period required for the growth of disturbances to a detectable size is inversely proportional to Ra_c^1/2.