This Brief Communication investigates the effect of variable viscosity and thermal conductivity of a nonisothermal, incompressible Newtonian fluid flowing under the effect of a constant pressure gradient in plane Poiseuille flow. The viscosity and thermal conductivity of the fluid exhibit linear temperature dependence and the effect of viscous heating is included in the analysis. Channel walls are kept at constant temperatures. Discretization is performed using a pseudospectral technique based on Chebyshev polynomial expansions. The resulting nonlinear, coupled boundary value problem is solved iteratively using Chebyshev pseudospectral method. (C) 2005 American Institute of Physics.