The conditions marking the onset of natural convection due to buoyant forces are investigated in the thermal entrance region of horizontal plane Couette flow. The base temperature profile produced by pure forced convection is approximated as a fourth order polynomial using the integral method. With this approximate base-temperature profile stability criteria are obtained by means of the local stability analysis, its modification, and the natural-amplification analysis. The last one takes into consideration the axial amplification rate of disturbances at the onset of thermal instability. This new concept is tested here for the first time. The consideration of axial amplification of disturbances makes the system more stable. It is shown that the results of the natural-amplification analysis agree well with the existing experimental data.