Certain hanging travel cosmetic carriers are able to hold objects as large as a travel blow-dryer, but due to the intensity of most types of travel, a hanging makeup bag cannot prevent your makeup items from clanking against one another.
Even a simple handheld blow dryer can help you get the job done.
Use a blow dryer on low heat while brushing hair straight (a larger barrel brush is preferred).
Then dry the area using a blow-dryer set on cool.
For those with wavy hair, you could air-dry your hair and then blast the roots with a blow dryer while holding them up for extra volume.