In the autumn of 1940, Bill Thompson left Hobbs, N.M., to enroll at the University of New Mexico. He came on a football scholarship and was a three-year letterman from 1941-43. Thompson was a second team All-Border Conference offensive tackle as a sophomore and first team as a junior. He was team captain as a senior in 1943 and was voted one of the outstanding players of the 1943 Sun Bowl.
Thompson was drafted by the Philadelphia Eagles of the NFL in 1945, but could not compete due to World War II, serving two-and-a-half years in the Navy.
He returned to Albuquerque in 1950 to enter the construction and real estate business. Thompson became a member of the Albuquerque Tennis Club in 1958 and later became its president. He twice won the New Mexico closed doubles championships for his age group, and volunteered his time to helping young people improve their skills on the court.