Heating at collisionless shocks due to the kinetic cross-field streaming instability, which is the finite beta (ratio of plasma to magnetic pressure) extension of the modified two stream instability, is studied. Heating rates are derived from quasi-linear theory and compared with results from particle simulations to show that electron heating relative to ion heating and heating parallel to the magnetic field relative to perpendicular heating for both the electrons and ions increase with beta. The simulations suggest that electron dynamics determine the saturation level of the instability, which is manifested by the formation of a flattop electron distribution parallel to the magnetic field. As a result, both the saturation levels of the fluctuations and the heating rates decrease sharply with beta. Applications of these results to plasma heating in simulations of shocks and the earth's bow shock are described.