  We present an 11 arcsec resolution map of the central two parsecs of the
Galaxy in the CO J =7->6 rotational transition. The CO emission shows rotation
about Sgr A*, but also evidence for non-circular turbulent motion and a clumpy
morphology. We combine our dataset with available CO measurements to model the
physical conditions in the disk. We find that the molecular gas in the region
is both warm and dense, with T~200-300 K, n_H2~50,000-70,000 cm^-3. The mass of
warm molecular gas we measure in the central two parsecs is at least 2000
M_solar, about 20 times the UV-excited atomic gas mass, ruling out an UV
heating scenario for the molecular material. We compare the available spectral
tracers with theoretical models and conclude that molecular gas is heated with
magneto-hydrodynamic shocks with v~10-20 kms and B~0.3-0.5 mG. Using the
conditions derived with the CO analysis, we include the other important
coolants--neutral oxygen and molecular hydrogen--to estimate the total cooling
budget of the molecular material. We derive a mass to luminosity ratio of 2-3
M_solar/ L_solar, which is consistent with the total power dissipated via
turbulent decay in 0.1 pc cells with v_rms~15 kms. These size and velocity
scales are comparable to the observed clumping scale and the velocity
dispersion. At this rate, the material near Sgr A* its dissipating its orbital
energy on an orbital timescale, and cannot last for more than a few orbits. Our
conclusions support a scenario in which the features near Sgr A* such as the
CND and northern arm are generated by infalling clouds with low specific
angular momentum.
