In this work, the heat transfer to the Couette-Poiseuille flow of a nonlinear viscoelastic fluid obeying the Giesekus model between parallel plates for the case where the lower plate is at rest and the upper one moves at constant velocity is studied. The momentum equation is analytically solved and the effect of dimensionless pressure gradient (G), Giesekus model parameter (alpha) and Deborah number (De) on the velocity profile is investigated. To analyze the influence of viscous dissipation on the heat transfer, the energy equation is solved by a finite volume method for two different thermal boundary conditions: uniform wall heat flux (Case 1) and constant wall temperature (Case 2). The results show strong effects of the viscoelastic parameters on the velocity and temperature profiles. It is observed that the viscous dissipation is responsible for the variation in the bulk fluid temperature and the effect of viscous heating depends on the values of dimensionless pressure gradient. (C) 2013 Elsevier B.V. All rights reserved.