Recently, Pinarbasi and Liakopoulos investigated the effect of variable viscosity on the interfacial stability of two-layer, plane, Poiseuille flow. Temperature and viscosity fluctuations were neglected based on the observation that their effect on the stability of single-layer, Poiseuille flow is very small. It is shown in the present work that temperature and viscosity fluctuations, under some conditions, have a significant effect on the interfacial mode of instability, especially for large Prandtl numbers.