Without more information it looks like you've got a difficult task. If James Hartt's service record doesn't show where he died, then it could have been in a field hospital near the battle, while in transit by wagon or rail car to another hospital, or in any of several hospitals across Georgia and Alabama.

Samuel H. Stout, the medical director for the Army of Tennessee, noted that after the battle of Chickamauga the hospitals in Atlanta had 1800 beds and received 10,000 patients.
". . .he sent many patients out of the department to the hospitals of other commands located in Montgomery, Macon, Columbus, and Augusta. After that, he related, he sent other patients to stay in private homes and to report to the hospital daily for treatment. Soldiers who were incapacitated but who did not need surgical treatment he furloughed, and sent those with slight wounds to convalescent camps."
from Confederate Hospitals on the Move: Samuel H. Stout and the Army of Tennessee by Glenna R. Schroeder-Lein, p.129

I wish you well with your search and I'm sorry I can't offer more assistance.

George Walker