We study the time dependent spectra produced via the bulk Compton process by a cold, relativistic shell of plasma moving (and accelerating) along the jet of a blazar, scattering on external photons emitted by the accretion disc and reprocessed in the broad line region. Bulk Comptonization of disc photons is shown to yield a spectral component contributing in the far UV band, and would then be currently unobservable. On the contrary, the bulk Comptonization of broad line photons may yield a significant feature in the soft X-ray band. Such a feature is time-dependent and transient, and dominates over the non thermal continuum only when: a) the dissipation occurs close to, but within, the broad line region; b) other competing processes, like the synchrotron self-Compton emission, yield a negligible flux in the X-ray band. The presence of a bulk Compton component may account for the X-ray properties of high redshift blazars that show a flattening (and possibly a hump) in the soft X-rays, previously interpreted as due to intrinsic absorption. We discuss why the conditions leading to a detectable bulk Compton feature might be met only occasionally in high redshift blazars, concluding that the absence of such a feature in the spectra of most blazars should not be taken as evidence against matter--dominated relativistic jets. The detection of such a component carries key information on the bulk Lorentz factor and kinetic energy associated to (cold) leptons.
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