A steam bath is wonderful after a cold or flu with coughing. The lungs love moisture and warmth and are relieved in this environment. As the article said, steam also helps break up congestion and helps the body get rid of excess mucus.
When I don't have the opportunity for a steam bath when I'm sick, I try to mimic it by adding hot water and a few drops of eucalyptus oil in a basin. I put my head over it, I cover with a towel to prevent the steam from escaping and breathe in. It makes me cough for a while but I feel so much better afterward. I can breathe again and my cough goes away.