 Thurmond was originally drafted by the San Diego Padres out of Texas A&M University in the 24th round of the 1978 MLB Draft, but he chose not to sign.He was then drafted by the Padres in the fifth round of the 1979 MLB Draft, and he signed that time.As a rookie in 1983, Thurmond went 7–3 with a 2.65 ERA, and he was tied for ninth in the 1983 NL Rookie of the Year Award voting.