There are a few things you can do to clean a curling iron barrel. The first is to remove any build-up on the inside of the barrel. This can be done by using a mild soap and water solution, or by using a brush and water solution. The second step is to clean the outside of the barrel. This can be done by using a mild soap and water solution, or by using a brush and water solution. The third step is to dry the barrel thoroughly. This can be done by using a hairdryer, or by taking it outside and drying it with an air conditioner.