The minimum Reynolds number,ReNc, below which all the two‐dimensional and monochromatic wave disturbances decay, is studied numerically for a thermally stratified plane Poiseuille flow. TheReNcis found to be sensitive to the change of Prandtl numberP. Under unstable stratification with Rayleigh number just below critical,ReNc&bartil;1000 is found forP≤10−3. ©1996 American Institute of Physics.