This article addresses the characteristics of convective heat transfer and radially imposed magnetic field on peristaltic flow of an incompressible Carreau fluid in a curved channel. Joule heating is also present. Mathematical analysis has been carried out under long wavelength and low Reynolds number considerations. Solutions of the resulting non-linear system for small values of Weissenberg number are constructed. The salient features of flow quantities are pointed out with particular focus to pumping, velocity, temperature and trapping. It is observed pressure gradient enhances for larger values of power law index parameter. The velocity and temperature are decreasing functions of radial magnetic field parameter. Further the impact of Weissenberg and Biot numbers on the temperature are opposite.