Why?You should probably remove the paint on the outside and re-paint it with high temp BBQ paint. A burn out will do that, or you can use chemical paint removers.
There is no need for high temp paint, however if you let your temps get away from you, say you don't get the lid on tight, it could reach temps that would burn the factory pain off. But if it where me I would just wash it and go to town on your build.You should probably remove the paint on the outside and re-paint it with high temp BBQ paint. A burn out will do that, or you can use chemical paint removers.