The influence of a temperature gradient across the channel on the steady-state simple shear flow of a nematic liquid crystal is investigated. The in-plane mean molecular orientation, velocity field and temperature profile are calculated on the basis of the Leslie-Ericksen theory. The dependence of the elasticity and viscosity on the temperature and the anisotropy of the heat conduction are taken into account. Results are obtained for a flow-aligning and a tumbling nematic. By shifting the temperature across the height of the channel so that the Leslie coefficient a3 changes sign at some point between the two bounding plates, the combination of flow-alignment and tumbling in a simply sheared liquid crystal is evaluated.