The heat transfer characteristics of a couple-stress fluid (CSF) in a two-dimensional asymmetric channel is analyzed. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. Mathematical modeling corresponding to the two-dimensional couple stress fluid is made. Analytical expressions for the axial velocity, stream function, heat transfer, and the axial pressure gradient are established using long wavelength assumption. Numerical computations have been carried out for the pressure rise per wavelength. The influence of various parameters of interest is seen through graphs on frictional forces, pumping and trapping phenomena, and temperature profile.