In this paper we study the effects of variable viscosity and thermal conductivity on the heat transfer in the pressure-driven fully developed flow of a slurry (suspension) between two horizontal flat plates. The fluid is assumed to be described by a constitutive relation for a generalized second grade fluid where the shear viscosity is a function of the shear rate, temperature and concentration. The heat flux vector for the slurry is assumed to follow a generalized form of the Fourier’s equation where the thermal conductivity k depends on the temperature as well as the shear rate. We numerically solve the governing equations of motion in the non-dimensional form and perform a parametric study to see the effects of various dimensionless numbers on the velocity, volume fraction and temperature profiles. The different cases of shear thinning and thickening, and the effect of the exponent in the Reynolds viscosity model, for the temperature variation in viscosity, are also considered. The results indicate that the variable thermal conductivity can play an important role in controlling the temperature variation in the flow.