What is done for a herniated disk in the thoracic area?

Nonop v surgery. Like a lot of disc herniations, they are found frequently in people with no pain & when the cause of symptoms they are treated non surgically with time, medication, activity modification, guided exercise & life style changes. Epidural steroid injections are an option. When pain does not get better & severe enough &/or creating neurologic issues then surgery which can be done several ways.
Rest to surgery. You should give this time as it should resolve, however if the pain is severe and there is spinal cord involvement with myelopathy than surgery is warranted.