<p>To predict the amplification factor of the Mack second mode instability in a hypersonic boundary layer, an amplification factor transport equation was developed within a RANS framework. Its production term is based on the approximate <i>N</i>-envelope method and modeled using compressible boundary layer profiles and linear stability theory (LST) analysis data. The transport equation is designed to use only local variables and does not require wall temperature as an explicit parameter. Furthermore, it accounts for the influence of wall temperature on the growth of the Mack second mode instability, which is a key contribution of this study. The amplification factor and the modified turbulence intermittency transport equations are coupled with a k-<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation> SST turbulence model as the transition model. The model was implemented in SU2, and grid experiments were performed. The predicted amplification factor was compared with the LST results with differences typically ranging from 0.4% to 17% across a range of flow and wall-temperature conditions, including non-uniform wall temperature distributions. Analysis of the transition model revealed that it is possible to predict the boundary layer transition with appropriate application of the critical amplification factors.</p>