  We extend previous work on gamma-ray burst (GRB) afterglows involving hot
thermal electrons at the base of a shock-accelerated tail. Using a
physically-motivated electron distribution based on first-principles
simulations, we compute broadband emission from radio to TeV gamma-rays. For
the first time, we present the effects of a thermal distribution of electrons
on synchrotron self-Compton (SSC) emission. The presence of thermal electrons
causes temporal and spectral structure across the entire observable afterglow,
which is substantively different from models that assume a pure power-law
distribution for the electrons. We show that early-time TeV emission is
enhanced by more than an order of magnitude for our fiducial parameters, with a
time-varying spectral index that does not occur for a pure power law of
electrons. We further show that the X-ray "closure relations" take a very
different, also time-dependent, form when thermal electrons are present; the
shape traced out by the X-ray afterglows is a qualitative match to observations
of the traditional decay phase.
