In the 1950s, Yost's own interests turned toward reviving the lost practice of manned hot-air ballooning. This technology had first been invented in France by in the late 1700s by pioneers led by the Montgolfier brothers, but under the Montgolfier system the balloon's air was heated by a ground fire prior to the balloon being released. The inherent danger of this type of balloon flight led to the system being abandoned when hydrogen and later helium became available.
One of Yost's key engineering insights was that a hot-air balloon could be made to carry its own fuel. The invention of relatively light burners fueled by bottled propane made it possible for the balloonist to re-heat the air inside the balloon for a longer flight. Yost’s invention improved modern hot-air balloons into semi-maneuverable aircraft. Yost's other hot-air balloon patents included nonporous synthetic fabrics, maneuvering vents, and deflation systems for landing. Yost also designed the distinctive “teardrop” shape of the hot air balloon envelope itself. This hot-air balloon image has become an icon, used for example on the standard license plate of motor vehicles registered in New Mexico.
On October 22, 1960, Yost made the first-ever free flight of a modern hot air balloon from Bruning, Nebraska. His balloon flew untethered for 1 hour and 35 minutes (1:35) with the aid of heat generated by a propane burner. The balloon's 40-foot (12 m) envelope was sewn from heat-resistant fabric especially selected by Yost for this purpose. After further refining and improving on this designs and materials, in 1963 Yost piloted the first modern balloon flight across the English Channel with crew member Don Piccard in a balloon later named the “Channel Champ.”
In 1976, Yost set 13 aviation world’s records for distance traveled and amount of time aloft in his attempt to cross the Atlantic Ocean —solo— by balloon. He designed and built his balloon, the “Silver Fox," himself, partly in his home garage. It featured a gondola that was shaped like a boat in the event that he would be forced down at sea — which is precisely what occurred. Although he had traveled far in excess of the distance needed to reach Europe from his launch point off the coast of Maine — his flight path began to point South rather than the hoped-for East direction due to inaccurate weather forecasting. The dream was achieved eight years later with Yost’s assistance in a Yost-built balloon, "The Balloon of Peace" flight from Caribou Maine to Montenotte Italy flown by Colonel Joseph Kittinger.
Yost also contributed to the advancement of the sport of ballooning and lighter-than-air flight. He helped to found the Balloon Federation of America (BFA) and assisted in the organization of the first US National Ballooning Championship at Indianola, Iowa.