In this paper we study the stability of nonisothermal plane Poiseuille flow by the method of small disturbances. A linear temperature profile and an exponential viscosity law are considered. In contrast to previously published studies, viscosity and temperature fluctuations are included in the formulation. 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 are presented for water. It is found that an imposed wall temperature difference, ΔT, is always destabilizing. The instability region in the wavenumber versus Reynolds number plane grows as ΔT increases. The critical Reynolds number decreases considerably compared with the isothermal case. However, the influence of Prandtl number, temperature fluctuations and viscosity fluctuations on the flow stability/instability is small.