Steam-heated Balloons?

In my world, one of the main methods of transportations is via hot-air balloon. These balloons are propelled by aluminum(or other lightweight metal, it doesn't really matter) steam engines, and the steam and heat produced by the engines also serve as the fire that heats the air in the balloon. Would the heat produced by an engine that favors being lightweight over being efficient be enough to lift some amount of passengers and cargo? (The airship does not need to travel quickly; 3-4 mph is enough)

EDIT: Some stats: The balloons are spherical with a diameter of 20 feet. They are expected to carry up to 450 pounds of passengers/luggage, in addition to the engine.

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Steam-heated Balloons?

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