[3] He then enrolled in Charleston Southern University, where he played college baseball for the Buccaneers, a member of the Big South Conference within NCAA Division I.

[9] Thornburg had a 7–0 win–loss record and 1.50 earned run average (ERA) with Wisconsin,[10][11] and represented the Timber Rattlers in the Midwest League All-Star Game.

[18] In his debut, Thorburg allowed back-to-back-to-back home runs to Colby Rasmus, José Bautista, and Edwin Encarnación.

Overall, with the 2012 Brewers, Thornburg appeared in eight games (three starts) without a win or loss, with a 4.50 ERA and 20 strikeouts and seven walks in 22 innings pitched.

[26] With the 2014 Brewers, Thornburg made 27 appearances, all in relief, compiling a 3–1 record with 4.25 ERA with 28 strikeouts and 21 walks in 29+2⁄3 innings pitched.

After starting the 2015 season with Milwaukee, Thornburg spent three months in Triple-A regaining his arm strength, before being recalled at the end of July.

With the 2015 Brewers, Thornburg made 24 appearances, all in relief, compiling an 0–2 record with 3.67 ERA, 34 strikeouts, and 12 walks in 34+1⁄3 innings pitched.

Prior to the 2016 season, the Brewers decided to use Thornburg as a full-time reliever rather than preparing him as a starter during spring training and in Triple-A.

[28] With the 2016 Brewers, Thornburg made a career-high 67 appearances, all in relief, compiling an 8–5 record with 2.15 ERA, 90 strikeouts, and 25 walks in 67 innings pitched.

Overall, in parts of five seasons with Milwaukee, Thornburg appeared in 144 games (ten starts), compiling a 14–9 record with 2.87 ERA; he had 220 strikeouts and 91 walks in 219+2⁄3 innings pitched.

On December 6, 2016, the Brewers traded Thornburg to the Boston Red Sox for Travis Shaw, Mauricio Dubon, Josh Pennington and a player to be named later.

During his rehabilitation assignments, Thornburg made 18 total appearances (one start), compiling an 0–1 record with 4.96 ERA, 16 strikeouts, and eight walks in 16+1⁄3 innings pitched.

[41] After being activated from the injured list, Thornburg declined a minor league assignment[42] and was released by the Red Sox on July 10.

[46] On December 31, 2019, Thornburg signed a minor league deal with the Cincinnati Reds that included an invitation to Spring Training.

On February 5, 2025, the Milwaukee Brewers hired Thornburg to serve as an associate coach for their Double-A affiliate, the Biloxi Shuckers.

Due to his velocity, size, over-the-top delivery, and repertoire, he has drawn favorable comparisons to Tim Lincecum.