How hot does a woodstove get?

First you need to check with your county codes to see exactly how it should be installed. I know where I grew up you were not allow dry wall the backing had to be some type of stone or brick, you also had to have it off the floor by 6 inches and inside some type of staging area, also made of either tile, stone or brick. The dimensions were also included and there was a safe distance the stove had to be from the wall. The heat of a stove can get extreme and even though sitting from it you wouldn't feel that full effect the drywall will. I think that the drywall itself would dry out even more with the extreme heat. After all it is only paper and chalktype of debris. I would definitely call county. If there is ever a fire and you did not adhere to the county codes your insurance company probably can choose not to compensate for any loss... Err on the side of caution.