This paper is concerned with the well-known phenomenon of hysteresis in the pressure drop-how rate relationship for steady-state nonisothermal pressure-driven flow of a non-Newtonian fluid in a channel. The fluid properties are described by a power law with an exponential temperature dependence of viscosity. Solutions of the motion and energy balance equations have been obtained in terms of two approximations for nonisothermal how in a finite-length cylindrical channel. The conditions of hysteresis and the related multivalued solution of a nonlinear boundary value problem have been found analytically. As part of the analysis, experimental studies have been carried out to verify the predictions of the analytical treatment.