In this paper the linear stability analysis of the interface between two Newtonian liquids with temperature‐dependent viscosity in plane Poiseuille flow is presented. A piecewise linear temperature profile is considered. The linearized equations describing the evolution of small, two‐dimensional disturbances are derived and the stability problem is formulated as an eigenvalue problem for a set of ordinary differential equations. The continuous eigenvalue problem is solved numerically by a pseudospectral method based on Chebyshev polynomial expansions. The method leads to a generalized matrix eigenvalue problem, which is solved by the QZ algorithm. Results on the onset of instability are presented in the form of stability maps for a range of thickness ratios, disturbance wave numbers, imposed temperature differences, constant‐temperature viscosity ratios, thermal conductivity ratios, and Reynolds numbers. Increasing the imposed temperature difference, constant‐temperature viscosity ratio, or Reynolds number can have a stabilizing or destabilizing effect, depending on the flow configuration (thickness ratio) and disturbance wavelength. Increasing the thermal conductivity ratio has a destabilizing effect on the interface for all configurations and disturbance wavelengths. ©1995 American Institute of Physics.