Ripening bananas artificially: What is the biological theory behind?
Ripening of bananas (and other fruits) is induced by acetylene and ethylene (Ethyne and Ethene) (see reference 1), which acts as a hormone and induces the ripening process. The incomplete combustion of the leaves produces ethylene, additionally the warmth of the process will help the enzymes as well. There is even a paper about this technique (although it is unfortunately not accessible), see reference 2 for more information. Smoking Chambers are routinely used in this process, see reference 3 and 4.

References:


Role of Ethylene in Fruit Ripening
Effects of smoking on some physiological changes in bananas.
Fruit Ripening
Technology for ripening fruits as important as marketing them