  To date, nearly all multi-wavelength modeling of long-duration gamma-ray
bursts has ignored synchrotron radiation from the significant population of
electrons expected to pass the shock without acceleration into a power-law
distribution. We investigate the effect of including the contribution of
thermal, non-accelerated electrons to synchrotron absorption and emission in
the standard afterglow model, and show that these thermal electrons provide an
additional source of opacity to synchrotron self-absorption, and yield an
additional emission component at higher energies. The extra opacity results in
an increase in the synchrotron self-absorption frequency by factors of 10--100
for fiducial parameters. The nature of the additional emission depends on the
details of the thermal population, but is generally observed to yield a
spectral peak in the optical brighter than radiation from the nonthermal
population by similar factors a few seconds after the burst, remaining
detectable at millimeter and radio frequencies several days later.
