The Survey of Water and Ammonia in the Galactic Center (SWAG) covers the Central Molecular Zone (CMZ) of the Milky Way at frequencies between 21.2 and 25.4 GHz obtained at the Australia Telescope Compact Array at $sim 0.9$ pc spatial and $sim 2.0$ km s$^{-1}$ spectral resolution. In this paper, we present data on the inner $sim 250$ pc ($1.4^circ$) between Sgr C and Sgr B2. We focus on the hyperfine structure of the metastable ammonia inversion lines (J,K) = (1,1) - (6,6) to derive column density, kinematics, opacity and kinetic gas temperature. In the CMZ molecular clouds, we find typical line widths of $8-16$ km s$^{-1}$ and extended regions of optically thick ($tau > 1$) emission. Two components in kinetic temperature are detected at $25-50$ K and $60-100$ K, both being significantly hotter than dust temperatures throughout the CMZ. We discuss the physical state of the CMZ gas as traced by ammonia in the context of the orbital model by Kruijssen et al. (2015) that interprets the observed distribution as a stream of molecular clouds following an open eccentric orbit. This allows us to statistically investigate the time dependencies of gas temperature, column density and line width. We find heating rates between $sim 50$ and $sim 100$ K Myr$^{-1}$ along the stream orbit. No strong signs of time dependence are found for column density or line width. These quantities are likely dominated by cloud-to-cloud variations. Our results qualitatively match the predictions of the current model of tidal triggering of cloud collapse, orbital kinematics and the observation of an evolutionary sequence of increasing star formation activity with orbital phase.
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