Margaret,
Thomas Hunt's Company, Alabama Militia, is in the "Records of Events" series of Broadfoot's AOR Supplement, Vol. 1 (serial No. 13), page 942. It was in service March 24 through April, probably 1862 militia call.
Thomas Hunt has three (3) compiled service records in the National Archives. One as Captain, Ala. Militia; one as pvt., R.N. Ware's Company, Talladega County Reserves Cavalry, which was a local defense unit; His final service was a sgt., Co. B, 4th Alabama Infanrty Reserves Regt.
It would appear he was from Talladega County. Check these three CSR's and you should have the whole story of his Confederate service.