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. In 1984, he had the best season of his career, going 14–8 with a 2.97 ERA as the Padres won the National League West. He lost Game 2 of the National League Championship Series, giving up 4 runs in 3 innings, but it didn't matter in the end as the Padres overcame an 0–2 deficit in the series to beat the Chicago Cubs 3 games to 2. He was also the losing pitcher in Game 1 of the 1984 World Series against the Detroit Tigers, giving up only three runs, but only lasting 5 innings. Thurmond also started Game 5, and although he only lasted 1/3 of an inning, he gave up three runs again but earned a no-decision this time. The 1985 season was sort of a let-down for Thurmond, as he went 7–11 with a 3.97 ERA and only started 23 of his 36 games. In 1986, Thurmond got off to a very rocky start, going 3–7 with a 6.50 ERA in his first 17 games. On July 9, 1986, he was traded to the Detroit Tigers for pitcher Dave LaPoint.
Detroit Tigers (1986–87)
Thurmond really turned things around upon his arrival in Detroit, although it was mostly in the bullpen. He finished the year with the Tigers 4–1, with a 1.92 ERA in 25 games. His next season with the Tigers was the first in which he didn't start a single game, as he went 0–1 with a 4.23 ERA in 48 games out of the bullpen. He made his final playoff appearance in Game 4 of the 1987 ALCS, pitching 1/3 of an inning without giving up a run. On February 26, 1988, the Tigers traded Thurmond to the Baltimore Orioles for Ray Knight.
Baltimore Orioles (1988–89)
Thurmond's first season with the Orioles, like their season in 1988, wasn't that great. He went 1–8 with a 4.58 ERA in 43 games while the Orioles finished last in the American League. The following season was better for Thurmond, as he went 2–4 with a 3.90 ERA in 49 games while pitching almost entirely out of the bullpen.
On February 1, 1990, Thurmond signed with the Houston Astros. However, he didn't pitch with them at all. Instead, he pitched in nine games for the Tucson Toros, the Astros' AAA affiliate, posting a 3.27 ERA with no decisions. On May 1, he was sent to the San Francisco Giants as part of a conditional deal.
San Francisco Giants (1990)
Thurmond pitched reasonably well out of the bullpen for the Giants, going 2–3 with a 3.34 ERA in 43 games. However, 1990 was his final year in the major leagues. In 1991, he finished his career with the Phoenix Firebirds, the Giants AAA affiliate, going 0–3 with a 3.42 ERA in 26 games.
Personal life
Thurmond currently resides in Katy, Texas, and works for an insurance business his father started.