Tennesseans in the Civil War, part 2 shows;
Appleton, Thomas - Pvt. B Co., 32nd Tennessee Infantry
Appleton, Thomas J. -Pvt. Co. H, 32nd Tennessee Infantry

I recall both of these companies being from the Lawrence and Giles Co., Tn. area. However the birthdate of 1848 would make either of these men only 13 yrs old in 1861 when the regiment was formed. The book "Strawfoot, the Life and Times of the 32nd Tennessee Infantry Regiment, 1861-1865" lists Thomas J. Appleton of Co. H as dying on Dec. 11, 1861. This most likely isn't the man you are seeking unless the birthdate you have is in error.
The Tennessee Archives has the microfilm records you can copy for these soldiers. If you live in TN it might be worth a trip to Nashville. If not you can get the same records from the National Archives.