This study investigates the pressure gradient-flow rate relationship for steady-state nonisothermal pressure-driven flow of a non-Newtonian fluid in a channel including the effect of viscous heating. The viscosity of the fluid depends on both temperature and shear-rate. Exponential dependence of viscosity on temperature is modeled through Arrhenius law. Non-Newtonian behaviour of the fluid is modeled according to the Carreau rheological equation. Flow governing motion and energy balance equations are coupled and the solution of this non-linear boundary value problem is found iteratively using a pseudospectral method based on Chebyshev polynomials. The effect of activation energy parameter and Brinkman number, as well as the power-law index and material time constant on the flow is studied. It is found that while the pressure gradient-flow rate graph is monotonic for certain ranges of flow controlling parameters, there is a large jump in the graph under certain values of these parameters. © 2002 Elsevier Science Ltd.