Heath went to Newton County High School and was drafted in the 27th round, 799th overall, as a senior by the New York Mets in 2003.

He played the offseason in the Arizona Fall League with the Mesa Solar Sox, appearing in 10 games with an 8.31 ERA.

[2][3] On April 5, 2010, Heath signed a minor league contract with the Chicago White Sox.

[6] He was returned to Charlotte on July 8, without having made an appearance for the White Sox, briefly becoming a phantom ballplayer.

[7] Heath was recalled on September 1, and made 3 appearances for Chicago, recording a 4.50 ERA with 1 strikeout in 2 innings.

On June 6, 2013, Heath was promoted to the major leagues to take the place of Brian Omogrosso, who was optioned to Charlotte.

[citation needed] In 30 games for Puebla, he logged a 3–3 record and 4.25 ERA with 32 strikeouts across 29+2⁄3 innings of relief.

On March 9, 2018, Heath signed with the Toyama Thunderbirds of the independent Baseball Challenge League of Japan.

Heath made 34 appearances for Seibu in 2019, compiling a 2–3 record and 3.73 ERA with 34 strikeouts across 31+1⁄3 innings pitched.

Heath made one appearance for the team in 2023, and didn't record an out after giving up two hits, two walks, and four earned runs.