The sub-mm bump observed in the spectrum of Sgr A* appears to indicate the existence of a compact emitting component within several Schwarzschild radii, rS, of the nucleus at the Galactic Center. This is interesting in view of the predicted circularized flow within 5-10 rS, based on detailed multi-dimensional hydrodynamic simulations of Bondi-Hoyle accretion onto this unusual object. In this paper, we examine the physics of magnetic field generation by a Keplerian dynamo subject to the conditions pertaining to Sgr A*, and show that the sub-mm bump can be produced by thermal synchrotron emission in this inner region. This spectral feature may therefore be taken as indirect evidence for the existence of this circularization. However, the required accretion rate in the Keplerian flow is orders of magnitude smaller than that predicted by the Bondi-Hoyle simulations. We speculate that rapid evaporation, in the form of a wind, may ensue from the heating associated with turbulent mixing of gas elements with large eccentricity as they settle down into a more or less circular (i.e., low eccentricity) trajectory. The spectrum of Sgr A* longward of 1-2 mm may be generated in the transition region outside of the Keplerian flow.