High-energy radiation can be generated by colliding a relativistic electron bunch with a high-intensity laser pulse—a process known as Thomson scattering. In the nonlinear regime the emitted radiation contains harmonics. For a laser pulse whose length is comparable to its wavelength, the carrier envelope phase changes the behavior of the motion of the electron and therefore the radiation spectrum. Here we show theoretically and numerically the dependency of the spectrum on the intensity of the laser and the carrier envelope phase. Additionally, we also discuss what experimental parameters are required to measure the effects for a beamed pulse.