This work is concerned with the peristaltic transport of the Johnson-Segalman fluid in an asymmetric channel with convective boundary conditions. The mathematical modeling is based upon the conservation laws of mass, linear momentum, and energy. The resulting equations are solved after long wavelength and low Reynolds number are used. The results for the axial pressure gradient, velocity, and temperature profiles are obtained for small Weissenberg number. The expressions of the pressure gradient, velocity, and temperature are analyzed for various embedded parameters. Pumping and trapping phenomena are also explored.