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We investigate the peristaltic motion of Carreau fluid in an asymmetric channel with convective boundary conditions. Mathematical formulation is first reduced in a wave frame of reference and then solutions are constructed by long wavelength and low Reynolds number conventions. Results of the stream function, axial pressure gradient, temperature and pressure rise over a wavelength are obtained for small Weissenberg number. Velocity and temperature distributions are analyzed for different parameters of interest. A comparative study between the results of Newtonian and Carreau fluids is given.