"We felt like we needed to do that for that stretch," Ventura said. "We are back even, feeling like we have the bullpen back to where we feel guys aren't overextended."
Heath made one appearance with the White Sox, against Cleveland on Saturday, and allowed one run over 1 2/3 innings. The 27-year-old was up for three games with the club last season in what was his first taste of the big leagues.
The White Sox will announce a corresponding move on Wednesday to fill out their 25-man roster.
Chris Toman is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.