A hot air balloon was an aircraft consisting of a fabric enclosure, the balloon, filled with air that is a higher temperature than the air outside the enclosure. The lower density of the hot air inside provides lift for the craft.
A hot air balloon was used by Kelemane in an attempt to send a letter to the object in the sky known as the "Ground Shaker". (VOY: "Blink of an Eye")
An image of several balloons was seen by Harry Kim, Neelix, and Kes while monitoring Earth communication after being transported to the year 1996. (VOY: "Future's End")
A hot air ballooon is also seen transiting a mountain range in the opening credits for Star Trek: Enterprise.