This study investigates the effect of variable thermal conductivity and variable viscosity on the flow characteristics and flow rates of an inelastic fluid, including viscous heating terms in the analysis. The exponential dependence of viscosity on temperature is modeled through Arrhenius law and shear rate dependence is modeled through Carreau rheological equation while it is assumed that the thermal conductivity varies linearly with temperature. Flow governing motion and energy balance equations are coupled and the solution is found iteratively facilitating a pseudospectral method based on the Chebyshev polynomial expansions. Effect of variable thermal conductivity and viscosity as well as the effect of power law index, material time constant, Brinkman and Peclet numbers on the velocity and temperature profiles are presented. Influence of the above parameters on the flow rate is also calculated. © 2008 Elsevier Ltd. All rights reserved.