We study theoretically the Čerenkov-type second-harmonic generation by a Gaussian beam in quadratic nonlinear media with periodically reverted ferroelectric domains. In particular, we consider the role of fundamental beam width on the harmonic emission process. We show that varying the beam width of the fundamental wave not only affects the strength of the emitted Čerenkov harmonic signal but also changes the sensitivity of the emission process to wavelength tuning.