  We examined the temperature (T) evolution of the optical conductivity spectra
of Sr$_3$Ir$_2$O$_7$ over a wide range of 10-400 K. The system was barely
insulating, exhibiting a small indirect bandgap of $\sim$0.1 eV. The low-energy
features of the optical d-d excitation (${\hbar}{\omega}$ $<$ 0.3 eV) evolved
drastically, whereas such evolution was not observed for the O K-edge X-ray
absorption spectra. This suggests that the T evolution in optical spectra is
not caused by a change in the bare (undressed) electronic structure, but
instead, presumably originates from an abundance of phonon-assisted indirect
excitations. Our results showed that the low-energy excitations were dominated
by phonon-absorption processes which involve, in particular, the optical
phonons. This implies that phonon-assisted processes significantly facilitate
the charge dynamics in barely insulating Sr$_3$Ir$_2$O$_7$.
