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The angular resolution (~10″) achieved by the Herschel Space Observatory ~3.5 m telescope at FIR wavelengths allowed us to roughly separate the emission toward the inner parsec of the galaxy (the central cavity) from that of the surrounding circumnuclear disk (the CND). The FIR spectrum toward Sgr A* is dominated by intense [O iii], [O i], [C ii], [N iii], [N ii], and [C i] fine-structure lines (in decreasing order of luminosity) arising in gas irradiated by the strong UV field from the central stellar cluster. The high-J CO rotational line intensities observed at the interface between the inner CND and the central cavity are consistent with a hot isothermal component at Tk ≈ 103.1 K and n(H2)≈ 104 cm−3. They are also consistent with a distribution of lower temperatures at higher gas density, with most CO at Tk≈300 K. The hot CO component (either the bulk of the CO column density or just a small fraction depending on the above scenario) likely results from a combination of UV and shock-driven heating. If UV-irradiated and heated dense clumps do not exist, shocks likely dominate the heating of the hot molecular gas component. Although this component is beam diluted in our FIR observations, it may be resolved at much higher angular resolution. An ALMA project using different molecular tracers to characterize UV-irradiated shocks in the innermost layers of the CND is ongoing. [ABSTRACT FROM PUBLISHER]