The zero-mean modulation produces the zero-mean conductive temperature drop but allows wall-induced buoyancy amplification from the time-dependent wall gradient. The question posed in the investigation concerns the high-frequency asymptotic onset of the stability under prescribed harmonic heat flux modulation and specifically if the relation \(\RL\sim C_q\omegac^{2}\) applies exclusively to the wall-layer criterion, whereas finite-amplitude stability holds throughout the depth of the layer. To find out the answer, the current study evaluates various characteristics such as neutral thresholds in terms of Floquet exponent, critical wavenumbers, high-frequency constants, nonlinear and strong stability thresholds, modified and alternative boundary conditions, variation in the Prandtl number, and DNS onset. The parameters are reformulated in terms of penetration depth, onset constant scaling, nonlinear separation constant, signed DNS threshold distance, and synchronization/subharmonic branches identification. The high-frequency onset is localized at first onset with \(\RL\sim C_q\omegac^{2}\) and \(k_c\sim\omegac^{1/2}\) for no-slip and no-stress cases with \(C_q=22.58\) and \(C_k=12.44\). With \(\omegac=100\), this yields respective onset estimates equal to \(2.258\times10^5\) and \(1.244\times10^5\). The above law alone does not guarantee nonlinear stability. The nonlinear thresholds depend on \(\Pran\) and the distant boundary effects, whereas the DNS cases determine whether growth, decay, finite-amplitude onset, and branches apply.