  We propose a time-dependent one-zone model based on a quasi-Maxwellian
`pile-up' distribution in order to explain the time-averaged high energy
emission of TeV blazars. The instantaneous spectra are the result of the
synchrotron and synchrotron self-Compton emission (SSC) of ultra-relativistic
leptons. The particle energy distribution function (EDF) is computed in a
self-consistent way, taking into account an injection term of fresh particles,
a possible pair creation term, and the particles radiative cooling. The source
term is not a usual power-law but rather a `pile-up' distribution, which can
result from the combination of a stochastic heating via second order Fermi
process and radiative cooling. To validate this approach, we have performed
time-averaged fits of the well-known TeV emitter Mrk 501 during the 1997
flaring activity period taking into account the attenuation of the high energy
component by cosmic diffuse infrared background (DIrB) and intrinsic absorption
via the pair creation process. The model can reproduce very satisfactorily the
observed spectral energy distribution (SED). A high Lorentz factor is required
to avoid strong pair production; in the case of smaller Lorentz factor, an
intense flare in the GeV range is predicted due to the sudden increase of soft
photons density below the Klein-Nishina threshold. The possible relevance of
such a scenario is discussed.
