It will be the second stint with the White Sox this season for Omogrosso, who had a 5.14 ERA and 14 strikeouts over 11 appearances from May 1-June 6.
In five appearances (7 2/3 innings) this season, Heath posted a whopping 11.74 ERA. In his third and most recent stint with the White Sox he made just one appearance, giving up three runs in two innings Wednesday at Minnesota on three hits and four walks.
Omogrosso will be available out of the White Sox's bullpen Friday for the start of a three-game series at Kansas City. In 10 appearances at Triple-A Charlotte this season, the 29-year old posted a 4.91 ERA with two saves and 14 strikeouts.