We present position-velocity strip maps of the Galactic Center region in the CO J=7 -> 6 and J=4 -> 3 transitions observed with the Antarctic Submillimeter Telescope and Remote Observatory (AST/RO) located at Amundsen-Scott South Pole Station. Emission from the two rotational transitions of 12CO was mapped at b=0o for 3.5o> l > -1.5o, on a 1' grid with a FWHM beamsize of 58'' at 806 GHz and 105'' at 461 GHz. The (CO J=4 -> 3)/(CO J=1 -> 0) line ratio map is almost featureless across the entire Galactic Center region. A Large Velocity Gradient (LVG) analysis shows that aside from the two special regions Sgr A and Sgr B, the photon-dominated regions within a few hundred parsecs of the Galactic Center are remarkably uniform in mean density and kinetic temperature at n = 2500 to 4000 \mathrmcm-3 and T = 30 to 45 K. The (CO J=7 -> 6)/(CO J=4 -> 3) line temperature ratios near Sgr B are a factor of two higher than those observed in the nuclear region of the starburst galaxy M82 (Mao et al. 2000), while the CO(J=7 -> 6)/CO(J=4 -> 3) line temperature ratios around Sgr A are similar to M82. The line ratio on large scales from the Galactic Center region is an order of magnitude less than that from M82.