  Recent interferometric observations have shown bright HCN emission from the
nu2=1 vibrational state arising in buried nuclear regions of galaxies,
indicating an efficient pumping of the nu2=1 state through absorption of 14
$\mu$m continuum photons. We have modeled the continuum and HCN vibrational
line emission in these regions, characterized by high column densities of dust
and high luminosities, with a spherically symmetric approach, simulating both a
central heating source (AGN) and a compact nuclear starburst (SB). We find that
when the H2 columns become very high, N_{H2}>~10^{25} cm-2, trapping of
continuum photons within the nuclear region dramatically enhances the dust
temperature (Tdust) in the inner regions, even though the predicted spectral
energy distribution as seen from outside becomes relatively cold. The models
thus predict bright continuum at millimeter wavelengths for luminosity surface
brightness (averaged over the model source) of ~10^{8} Lsun pc^{-2}. This {\it
greenhouse} effect significantly enhances the mean mid-infrared intensity
within the dusty volume, populating the nu2=1 state to the extent that the HCN
vibrational lines become optically thick. AGN models yield higher Tdust in the
inner regions and higher peak (sub)millimeter continuum brightness than SB
models, but similar HCN vibrational J=3-2 and 4-3 emission owing to both
optical depth effects and a moderate impact of high \tdust\ on these low-J
lines. The observed HCN vibrational emission in several galaxies can be
accounted for with a HCN abundance of ~10^{-6} (relative to H2) and luminosity
surface brightness in the range (0.5-2)x10^{8}$ Lsun pc^{-2}, predicting a
far-infrared photosphere with Tdust}~80-150 K --in agreement with the values
inferred from far-infrared molecular absorption.
