He was one of twelve pilots who flew the North American X-15, an experimental spaceplane jointly operated by the United States Air Force and NASA.

Thompson was hired as an engineer at the flight research facility on March 19, 1956, when it was still under the auspices of the National Advisory Committee for Aeronautics (NACA).

He flew it a total of 47 times, and also made the first five flights of the all-metal Northrop M2-F2 lifting body, beginning July 12, 1966.

They were flown at Dryden to study and validate the concept of safely maneuvering and landing a low lift-over-drag vehicle designed for reentry from space.

Thompson was also one of the 12 NASA, Air Force, and Navy pilots to fly the North American X-15 rocket-powered research aircraft between 1959 and 1968.

He flew the aircraft 14 times during the following two years, reaching a maximum speed of 3,712 mph (Mach 5.48) and a peak altitude of 214,100 feet on separate flights.

In 1962 the U.S. Air Force selected Thompson to be the only civilian test pilot to fly in the X-20 Dyna-Soar program that was intended to launch a human into Earth orbit and recover with a horizontal ground landing.

He also received the 1967 Octave Chanute Award from the American Institute of Aeronautics and Astronautics (AIAA) for his lifting-body research.