  Previous studies of the protoplanetary disk HD 163296 revealed that the
morphology of its sub-au infrared emission encompasses the terminal sublimation
front of dust grains, referred to as the inner rim, but also extends into the
(supposedly) dust-free region within it. Here, we present a set of radiative
hydrostatic simulations of the inner rim in order to assess how much the rim
alone can contribute to the observed interferometric visibilities $V$,
half-light radii $R_{\mathrm{hl}}$, and fractional disk fluxes $\mathcal{F}$ in
the wavelength range $1.5$--$13\,\mu\mathrm{m}$. In our set of models, we
regulate the cooling efficiency of the disk via the boundary condition for
radiation diffusion and we also modify the shape of the sublimation front. We
find that when the cooling efficiency is reduced, the infrared photosphere at
the rim becomes hotter, leading to an increase of $R_{\mathrm{hl}}$ sufficient
to match the observations. However, the near-infrared disk flux is typically
too low ($\mathcal{F}\simeq0.25$ at $1.5\,\mu\mathrm{m}$), resulting in H-band
visibility curves located above the observed data. We show that the match to
the H-band observations up to moderate baselines can be improved when a
wall-shaped rather than curved sublimation front is considered. Nevertheless,
our model visibilities always exhibit a bounce at long baselines, which is not
observed, confirming the need for additional emission interior to the rim. In
summary, our study illustrates how the temperature structure and geometry of
the inner rim needs to change in order to boost the rim's infrared emission.
