Transition reversal—the sometimes observed decrease in transition Reynolds number with surface cooling—has been thought to be other than a Tollmien—Schlichting instability phenomenon since it could not be reconciled with the results of the Dunn and Lin calculations of the temperatures required for complete stabilization of supersonic flat plate boundary layers. Recent theoretical developments in the stability of compressible boundary layers to Tollmien—Schlichting waves, however, point out the importance of considering in the analysis the hitherto neglected temperature fluctuations and thermal boundary condition. Accordingly, the temperatures required for complete stabilization of flat plate boundary layers to both two‐and three‐dimensional disturbances have been recomputed. The new required temperatures are all below the Dunn—Lin values. In the usual diagram of surface temperature vs stream Mach number there are two loops of complete stability. The trends suggested by this diagram tend to substantiate the experimentally observed transition reversal phenomenon. The results are compared with available wind tunnel and flight data.